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In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the...

In analytic geometry, the isoperimetric ratio of a simple closed curve in the Euclidean plane is the ratio L2/A, where L is the length of the curve and...

In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large-scale behavior of the manifold...

notion of a Dehn function is motivated by isoperimetric problems in geometry, such as the classic isoperimetric inequality for the Euclidean plane and,...

In geometry, the isoperimetric point is a triangle center — a special point associated with a plane triangle. The term was originally introduced by G...

In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov, and later independently by Christer Borell, states...

In mathematics, the Cheeger constant (also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck"...

In Riemannian geometry, the Cheeger isoperimetric constant of a compact Riemannian manifold M is a positive real number h(M) defined in terms of the minimal...

geometry and geometric measure theory which states that the classical isoperimetric inequality may be generalized to spaces of nonpositive sectional curvature...

does not hold, then the isoperimetric point possesses the equal detour property as well. The equal detour point, isoperimetric point, the incenter and...

least perimeter that encloses the maximum area. This is known as the isoperimetric inequality, which states that if a rectifiable Jordan curve in the Euclidean...

it satisfies a linear isoperimetric inequality. Moreover, there is an isoperimetric gap in the possible spectrum of isoperimetric functions for finitely...

low degree and high expansion parameters. The edge expansion (also isoperimetric number or Cheeger constant) h(G) of a graph G on n vertices is defined...

Jennifer. "The Sagacity of Circles: A History of the Isoperimetric Problem - The Isoperimetric Problem in Literature | Mathematical Association of America"...

inequality is a functional isoperimetric inequality for the canonical Gaussian measure. It generalizes the Gaussian isoperimetric inequality. The equation...

restating the problem as a minimization of the Rayleigh quotient. The isoperimetric inequality can be deduced from the Pólya–Szegő inequality with p = 1...

subdivisions, such as neighborhoods or voting districts (something isoperimetric rules would discourage); and it allows concave coastline districts,...

theory field of mathematics, Talagrand's concentration inequality is an isoperimetric-type inequality for product probability spaces. It was first proved...

1983). Pu's inequality bears a curious resemblance to the classical isoperimetric inequality L 2 ≥ 4 π A {\displaystyle L^{2}\geq 4\pi A} for Jordan curves...

Wirtinger. It was used by Adolf Hurwitz in 1901 to give a new proof of the isoperimetric inequality for curves in the plane. A variety of closely related results...

elliptic equations and reaction-diffusion equations, and for her book on isoperimetric inequalities. She is a professor emerita of mathematics at the University...

William (1894). "Isoperimetrical problems". Nature Series: Popular Lectures and Addresses. II: 571–592. Chavel, Isaac (2001). Isoperimetric inequalities....

formula is used, together with the Brunn–Minkowski theorem, to prove the isoperimetric inequality. It is named after Hermann Minkowski and Jakob Steiner. Let...

1 ) {\textstyle c(X)={\frac {\mu (K)^{1/n}}{S(K)^{1/(n-1)}}}} . The isoperimetric inequality states that this is maximized on Euclidean balls. The Brunn–Minkowski...

The Fisher information matrix plays a role in an inequality like the isoperimetric inequality. Of all probability distributions with a given entropy, the...

includes the study of geometric aspects of Sobolev-type inequalities, isoperimetric inequalities, and the Rayleigh–Faber–Krahn inequality. She is an assistant...

number, minus 1. In every polygon with perimeter p and area A , the isoperimetric inequality p 2 > 4 π A {\displaystyle p^{2}>4\pi A} holds. For any two...

{\displaystyle A^{*}} . These algorithms show up in solving the classical isoperimetric inequality problem, which asks: Given all two-dimensional shapes of...

curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense) Introductio in analysin infinitorum...

be calculated using the "Surveyor's formula" (shoelace formula). The isoperimetric inequality states that, for a closed curve of length L (so the region...

circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality. More precisely, consider a planar simple closed curve of...

When the outer Soddy circle has negative curvature, its center is the isoperimetric point of the triangle: the three triangles formed by this center and...

boundary. These boundaries and their sizes are particularly relevant for isoperimetric problems in graphs, separator theorems, minimum cuts, expander graphs...

optimal transport techniques to get improved versions of the anisotropic isoperimetric inequality, and obtained several other important results on the stability...

(n-1)} -sphere of radius 1. The hyperbolic space also satisfies a linear isoperimetric inequality, that is there exists a constant i {\displaystyle i} such...

{\displaystyle T} and perimeter p {\displaystyle p} are related by the isoperimetric inequality p 2 > 12 3 T . {\displaystyle p^{2}>12{\sqrt {3}}T.} This...

inequality is closely related to the Brunn–Minkowski inequality and the isoperimetric inequality. Let K and L be two n-dimensional convex bodies in n-dimensional...

(and therefore with the smallest SA:V) is a ball, a consequence of the isoperimetric inequality in 3 dimensions. By contrast, objects with acute-angled spikes...

eigenvalue of its Laplacian. The Cheeger constant (also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph...

function. The formula plays a decisive role in the modern study of isoperimetric problems. For smooth functions the formula is a result in multivariate...

lines enjoying the maximum-minimum property, or the solution of the isoperimetric problem in the broadest sense] (in Latin). Geneva, Switzerland: Marc...

Archimedes gave the first known precise definition of convexity. The isoperimetric problem, a recurring concept in convex geometry, was studied by the...

asymptotically n/2 log n; with Imre Leader he proved basic discrete isoperimetric inequalities; with Richard Arratia and Gregory Sorkin he constructed...

which gives a relation between the first positive eigenvalue and an isoperimetric constant (the Cheeger constant). Many versions of the inequality have...

automorphism α of Fn the mapping torus group of α satisfies a quadratic isoperimetric inequality; a proof of algorithmic solvability of the conjugacy problem...

the figures have the same convex hull; the big, first hexagon. The isoperimetric problem is to determine a figure with the largest area, amongst those...

the sphere is the one having the greatest volume. It follows from isoperimetric inequality. These properties define the sphere uniquely and can be seen...

SDE which has a weak solution but no strong solution. The Gaussian isoperimetric inequality (proved by Vladimir Sudakov and Tsirelson, and independently...

measure σn coincides with (normalized) Haar measure on Sn. There is an isoperimetric inequality for the sphere with its usual metric and spherical measure...

two-dimensional surface Circumgon – Geometric figure which circumscribes a circle Isoperimetric inequality – Geometric inequality applicable to any closed curve Perimeter-equivalent...

The first example goes back to Paul Lévy. According to the spherical isoperimetric inequality, among all subsets A {\displaystyle A} of the sphere S n...

relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality. If a circle of radius r is centred at the vertex of an angle...

Reviews characterized them as ``remarkable foundational results regarding isoperimetric functions of finitely presented groups and their connections with the...

Lévy–Khintchine representation Lévy–Itô decomposition Lévy flight local time Isoperimetric inequality on a sphere Lévy's characterisation of Brownian motion "Médaille...

Dido, Texas, a ghost town in Tarrant County, Texas Dido's problem, the isoperimetric problem in mathematics All pages with titles containing dido This disambiguation...

decreases monotonically, until it becomes convex. Once convex, the isoperimetric ratio of the curve decreases as the curve converges to a circular shape...

geometry and information theory. He has achieved important results about isoperimetric problems, concentration of measure and other high-dimensional phenomena...

mathematics, Wiley 1964 (ed. Edwin F. Beckenbach) with Gábor Szegő: Isoperimetric inequalities in mathematical physics, Princeton, Annals of Mathematics...

gravitation, Hele-Shaw flows of viscous fluids, and purely mathematical isoperimetric problems, and interest in them seems to be steadily growing. They were...

Gaussian copula Gaussian measure Gaussian correlation inequality Gaussian isoperimetric inequality Gauss's inequality Gauss-Helmert model The normal distribution...

inequalities for the first eigenvalue of the Laplacian and rigidity in some isoperimetric type inequalities.". In 2018 he was awarded the Stampacchia Medal. In...

Riemannian manifold M {\displaystyle M} which satisfies the same sharp isoperimetric inequality as a complete simply connected space form of constant sectional...

ISBN 978-1-4357-1633-9. Although some authors speak of a general method of solving "isoperimetric problems", the eighteenth-century meaning of this expression amounts...

of the Mathematical Association. She was known for her research on isoperimetric inequalities, her work in mathematics education, and her publications...

brachistochrone problem Solution to the tautochrone problem Solution to isoperimetric problems Calculating geodesics Finding minimal surfaces and solving...

thus cause burning. Zenodorus is known for authoring the treatise On isoperimetric figures, now lost. Many of its propositions are known from Theon of...

variables. In 2004, he received the EMS Prize (prize presentation: isoperimetric inequalities, probability measures and convex geometry) for his leading...

bubble has locally-minimal area. The double bubble theorem extends the isoperimetric inequality, according to which the minimum-perimeter enclosure of any...

in his very first paper in 1926, when he showed that the classical isoperimetric inequality holds on non-positively curved surfaces. This established...

generalizes and adapts Fubini's theorem to geometric measure theory. The isoperimetric inequality, which states that the smallest possible circumference for...

properly by isometries on a CAT(0) space, although they have quadratic isoperimetric inequality. Automorphism groups of free groups of rank ≥ 3 {\displaystyle...

Prize (1999) Scientific career Fields Combinatorics Thesis Discrete Isoperimetric Inequalities and Other Combinatorial Results  (1989) Doctoral advisor...

congruence sec ⁡ A 2 {\displaystyle \sec {\tfrac {A}{2}}} 1987 X175 Isoperimetric point sec ⁡ A 2 cos ⁡ B 2 cos ⁡ C 2 − 1 {\displaystyle \sec {\tfrac...

linear isoperimetric inequality; it turns out that having such an isoperimetric inequality characterises Gromov-hyperbolic spaces. Linear isoperimetric inequalities...

m-dimensional Hausdorff measure of A. Gaussian isoperimetric inequality Geometric measure theory Isoperimetric inequality in higher dimensions Minkowski–Bouligand...

when ℓ = w {\displaystyle \ell =w\,} , the rectangle is a square. The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter...

multiplicity ( n k ) {\displaystyle {\binom {n}{k}}} in both cases. has isoperimetric number h ( G ) = 1 {\displaystyle h(G)=1} . The family Q n {\displaystyle...

Hadwiger–Finsler inequality Hinge theorem Hitchin–Thorpe inequality Isoperimetric inequality Jordan's inequality Jung's theorem Loewner's torus inequality...

{\displaystyle \pi d} for the perimeter of a circle given its diameter. By the isoperimetric inequality and Barbier's theorem, the circle has the maximum area of...

and pass through the third], pp. 128–144 Veldkamp, G. R. (1985), "The Isoperimetric Point and the Point(s) of Equal Detour in a Triangle", The American...

area and perimeter enclosed by a quadrilateral, then the following isoperimetric inequality holds: 16 A ≤ P 2 {\displaystyle 16A\leq P^{2}} with equality...

particularly in high dimensions. Basic examples include "isomorphic isoperimetric inequalities" which are closely linked to the concentration of measure...

Gromov, M.; Milman, V. D. (1983). "A topological application of the isoperimetric inequality" (PDF). American Journal of Mathematics. 105 (4): 843–854...

area. The sphericity of a sphere is unity by definition and, by the isoperimetric inequality, any shape which is not a sphere will have sphericity less...

University of Grenoble (Institut Fourier). His research deals with isoperimetric inequalities in Riemann geometry, rigidity issues, and the Laplace operator...

X(22) Exeter point X(39) Brocard midpoint X(40) Bevan point X(175) Isoperimetric point X(176) Equal detour point X(356) Morley center X(357) First Morley–Taylor–Marr...

contributions to the study of the Biham–Middleton–Levine traffic model [AB] and isoperimetric inequalities on Riemannian manifolds[BC]. "Prof. Itai Benjamini", Honors...

Association of America, p. 155, ISBN 978-0-88385-352-8 Firey, W. J. (1960), "Isoperimetric ratios of Reuleaux polygons", Pacific Journal of Mathematics, 10 (3):...

differential geometry, the two integrated in a theory of minimal surfaces, isoperimetric inequality, and other issues in the areas of astronomy, geometry, cartography...

assumptions. Around the same time, a similar inequality was obtained by isoperimetric methods by Mikhael Gromov, although his result is weaker than Li and...

mathematics (2000), both from Dartmouth College. His PhD thesis was entitled "Isoperimetric numbers of certain Cayley graphs associated to PSL (2, [zeta subscript...

dimension Inductive dimension Lebesgue covering dimension Packing dimension Isoperimetric dimension Measurements of objects can be referred to as dimensions Dimensions...

Whitney: Loomis, L. H.; Whitney, H. (1949). "An inequality related to the isoperimetric inequality". Bull. Amer. Math. Soc. 55 (10): 961–962. doi:10...

the famous Steiner's chain of tangential circles, and a proof of the isoperimetric theorem (later a flaw was found in the proof, but was corrected by Weierstrass)...

Sobolev inequalities, Hoffman and Spruck were also able to derive new isoperimetric inequalities for submanifolds of Riemannian manifolds.[HS74] It is well...

physics and chemistry in statistics Exterior dimension Hurst exponent Isoperimetric dimension Metric dimension Order dimension q-dimension Fractal (q =...

geometric measure theory concerning the generalization of the classical isoperimetric inequality to spaces of nonpositive sectional curvature Cauchy–Hadamard...

Caputo, Michael R. (2005). "Necessary and Sufficient Conditions for Isoperimetric Problems". Foundations of Dynamic Economic Analysis : Optimal Control...

groups include: the growth rate of a finitely generated group; the isoperimetric function or Dehn function of a finitely presented group; the number...

inequality yields, in the limit case, with p = 1 , {\displaystyle p=1,} the isoperimetric inequality. Also, one can use some relations with harmonic functions...

MR 2231924 Andrews, Ben; Bryan, Paul (2010), "Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere", Calc. Var....

graphometer, hexameter, hygrometer, hygrometry, isodiametric, isometric, isoperimetric, meter, metre, metric, metrology, metronome, monosymmetric, parameter...

of as analogous to Bonnesen's inequality with isoperimetric defect, a strengthening of the isoperimetric inequality. A number of new inequalities of this...

polar body of its projection body. There are two remarkable affine isoperimetric inequality for this body. Petty (1971) proved that for all convex bodies...

stability of hypersurfaces and of minimal surfaces, topology of manifolds, isoperimetric problems, minimal submanifolds of a sphere, and manifolds of constant...

| {\displaystyle 2|\pi _{j}(E)|\leq |\partial E|} , we get a loose isoperimetric inequality: | E | d − 1 ≤ 2 − d | ∂ E | d {\displaystyle |E|^{d-1}\leq...

{\displaystyle \mathbb {R} ^{n}} . When n = 2 {\displaystyle n=2} , by the isoperimetric inequality, this probability is upper bounded by 1 2 {\displaystyle...

arbelos. Book V discusses isoperimetric figures, summarizing otherwise lost works by Zenodotus and Archimedes on isoperimetric plane and solid figures,...

Estimation of covariance matrices Fractional Brownian motion Gaussian isoperimetric inequality Gaussian measure / anl Gaussian random field Gauss–Markov...

be obtained by substituting the altitude formula. A version of the isoperimetric inequality for triangles states that the triangle of greatest area among...

by using the theory of strongly regular graphs. If q is prime, the isoperimetric number i(G) of the Paley graph satisfies the following bounds: q − q...

dynamics and the calculus of variations, the Chaplygin problem is an isoperimetric problem with a differential constraint. Specifically, the problem is...

network connection described above, there are important connections to isoperimetric inequalities, see more here, functional inequalities such as Sobolev...

of Analytical Functions, Leonhard Euler's Elements of Algebra and Isoperimetrical Problems, Alexis Clairaut's Figure of the Earth, Gaspard Monge's Application...

shots by O ( log ⁡ log ⁡ n ) {\displaystyle O(\log \log n)} . By the isoperimetric inequality, the curve of constant width in the Euclidean plane with...

59 (2001), no. 2, 177–267. Hoffman, David; Spruck, Joel Sobolev and isoperimetric inequalities for Riemannian submanifolds. Comm. Pure Appl. Math. 27...

In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split...

Möbius transformations. Circular triangles give the solution to an isoperimetric problem in which one seeks a curve of minimum length that encloses three...

Yang, Deane; Zhang, Gaoyong (2000), " L p {\displaystyle L_{p}} affine isoperimetric inequalities", Journal of Differential Geometry, 56 (1): 111–132, doi:10...

polyhedra studied in 1935 by Michael Goldberg as a possible solution to the isoperimetric problem of maximizing the volume for a given number of faces (16 in...

mentioned above, is diffusion. Among others are: the geometry of numbers, isoperimetric problems, recurrence of random walks, quadratic reciprocity, the central...

approaching infinity. Another very common shape factor is the circularity (or isoperimetric quotient), a function of the perimeter P and the area A: f circ = 4...

It is a standard tool in integral geometry and has applications in isoperimetric and rigidity results. The formula is named after Luis Santaló, who first...

densities and the isoperimetric inequality. Ch. II. Integral geometry on surfaces including Blaschke's formula and the isoperimetric inequality on surfaces...

ISBN 0-8176-3364-2, MR 0904286 Harper, L. H. (1966), "Optimal numberings and isoperimetric problems on graphs", Journal of Combinatorial Theory, 1 (3): 385–393...

consequence of the Tits alternative). Hyperbolic groups satisfy a linear isoperimetric inequality. Hyperbolic groups are always finitely presented. In fact...

Catherine Bandle (born 1943), Swiss expert on differential equations and isoperimetric inequalities Selenne Bañuelos (born 1985), Mexican-American mathematician...

transport with quadratic cost. At this point, a very short proof of the isoperimetric inequality appears. The inequality states that among all open sets of...

expansion is bounded away from zero. expansion 1.  The edge expansion, isoperimetric number, or Cheeger constant of a graph G is the minimum ratio, over...

Mathematical Society. pp. 143–152. Chanillo, Sagun; Yang, Paul C. (2009). "Isoperimetric and Volume Comparison theorems on CR manifolds". Annali della Scuola...

methods to bound stochastic processes. He discovered new aspects of the isoperimetric and concentration of measure phenomena for product spaces, by obtaining...

intercept, y-intercept, x-intercept Intersection number Intrinsic equation Isoperimetric inequality Jordan curve Jordan curve theorem Knot Limit cycle Linking...

two umbilical points. Cartan–Hadamard conjecture: can the classical isoperimetric inequality for subsets of Euclidean space be extended to spaces of nonpositive...

Nine-point circle Circle points segments proof Mrs. Miniver's problem Isoperimetric theorem Annulus Ptolemaios' theorem Steiner chain Eccentricity Ellipse...

Fernando Codá Marques and André Neves. Isoperimetric inequalities. In 1939 Schmidt proved that the classical isoperimetric inequality for curves in the Euclidean...

are the critical points for the mean curvature flow; minima solve the isoperimetric problem. For manifolds embedded in a Kähler–Einstein manifold, if the...

distance from the point p. The proof utilizes the coarea inequality, the isoperimetric inequality, the cone inequality, and the deformation theorem of Herbert...

supervision of Xavier Fernique. He has done important research on the isoperimetric inequality in analysis and probability theory. In 2010, he received...

al. An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem. Vol. 259. Springer Science & Business Media, 2007. Danielli...

perimeter, the one with the largest area is the square. This is called the isoperimetric theorem for quadrilaterals. It is a direct consequence of the area inequality...

Riemannian metric. Isometry is a surjective map which preserves distances. Isoperimetric function of a metric space X {\textstyle X} measures "how efficiently...

put the Levy-Gromov isoperimetric inequality into this setting. Much of his current work deals with various aspects of isoperimetric inequalities and manifolds...

Grierson John Gunn George Harvey William Jory Henwood J. F. W. Herschel ("Isoperimetrical Problems", "Mathematics") Samuel Hibbert John Hodgson James Innes David...

generalized submanifolds. Moreover, they identified new results on the isoperimetric problem and its relation to the Sobolev embedding theorem. Their paper...

Carathéodory showed how to extend solutions to discontinuous cases and studied isoperimetric problems. Previously, between the mid-1700s to the mid-1800s, Leonhard...

Mathematical Society; 2nd edn. 1955 Pólya, George; Szegő, Gábor (2016) [1951], Isoperimetric problems in mathematical physics, Annals of Mathematics Studies, vol...

JSTOR 2951832. Sapir, Mark V.; Birget, Jean-Camille; Rips, Eliyahu (2002). "Isoperimetric and isodiametric functions of groups". Annals of Mathematics. 2. 156...

24 March 2015. Retrieved 10 January 2016. Kleiner, Bruce (1992). "An isoperimetric comparison theorem". Inventiones Mathematicae. 108 (1): 37–47. Bibcode:1992InMat...

of what makes a shape compact. A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle...

Mathematicians in Zurich. Hoffman, David; Spruck, Joel. Sobolev and isoperimetric inequalities for Riemannian submanifolds. Comm. Pure Appl. Math. 27...

isodiametric inequality or Bieberbach inequality, a relative of the isoperimetric inequality, states that, for a given diameter, the planar shape with...

known for his work in convex geometry, and a generalization of the isoperimetric inequality, which establishes a relationship between the radii of inscribed...

and low efficiency gap would result in low Polsby–Popper compactness. Isoperimetric inequality Roundness Polsby, Daniel D.; Popper, Robert D. (1991). "The...

August 12, 2011. Retrieved October 13, 2011. Payne, L. E. (1967). "Isoperimetric inequalities and their applications". SIAM Review. 9 (3): 453–488. Bibcode:1967SIAMR...

automorphism α of Fn the mapping torus group of α satisfies a quadratic isoperimetric inequality; a proof of algorithmic solvability of the conjugacy problem...

doi:10.2140/pjm.1980.90.201. MR 0599332. Varopoulos, N.Th (1985). "Isoperimetric inequalities and Markov chains". J. Funct. Anal. 63 (2): 215–239. doi:10...

from Геометрические неравенства, Nauka 1980. Burago, Yu. D. (1970). Isoperimetric inequalities in the theory of surfaces of bounded external curvature...

David; Gnepp, Andrei; Ng, Ting; Spivack, John; Yoder, Cara (2005), "The isoperimetric problem on some singular surfaces", Journal of the Australian Mathematical...

Quarterly of Applied Math., 6 (1948), pp. 267, 277. G. Pólya and G. Szegő, Isoperimetric inequalities in Mathematical Physics (Princeton Univ.Press, 1951)....

nilpotent groups. The second part has four chapters, on braid groups, isoperimetric inequalities, geometric finiteness, and the fundamental groups of three-dimensional...

algorithms of this category are normalized cuts, random walker, minimum cut, isoperimetric partitioning, minimum spanning tree-based segmentation, and segmentation-based...

condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals...

two other squares that share a vertex. List of triangle inequalities Isoperimetric inequality Martin Lukarevski, The circummidarc triangle and the Finsler-Hadwiger...

astonishing link between Mahler's conjecture in convexity theory and an isoperimetric-type inequality involving symplectic capacities (with R. Karasev and...

diameter Mossinghoff, Michael J. (2011), "Enumerating isodiametric and isoperimetric polygons", Journal of Combinatorial Theory, Series A, 118 (6): 1801–1815...

S={\frac {a^{2}+b^{2}+c^{2}}{4\Delta }}} . List of triangle inequalities Isoperimetric inequality Hadwiger–Finsler inequality Claudi Alsina, Roger B. Nelsen:...

1007/s00440-014-0568-6. ISSN 0178-8051. Toshiro, Watanabe (1983). "The isoperimetric inequality for isotropic unimodal Lévy processes". Z. Wahrsch. Verw...

can then be thought of as the isosystolic defect, analogous to the isoperimetric defect of Bonnesen's inequality. This approach therefore produces the...

2\exp {\bigg (}{\frac {-u^{2}}{2\sigma _{T}^{2}}}{\bigg )}} . Gaussian isoperimetric inequality "Gaussian Inequalities". Random Fields and Geometry. Springer...

caustic. The oriented area of the Wigner caustic improves the classical isoperimetric inequality. A non-singular hedgehog has a unique tangent line in each...

Gauss–Markov theorem Gauss–Newton algorithm Gaussian function Gaussian isoperimetric inequality Gaussian measure Gaussian noise Gaussian process Gaussian...

limit point is itself a compact set). As an example of its use, the isoperimetric problem can be shown to have a solution. That is, there exists a curve...

triangle Inellipse Integer triangle Isodynamic point Isogonal conjugate Isoperimetric point Isosceles triangle Isosceles triangle theorem Isotomic conjugate...

number theoryPages displaying short descriptions of redirect targets Isoperimetric problem – Geometric inequality applicable to any closed curve Japanese...

first Steklov eigenvalue in terms of conformal volumes, in addition to isoperimetric inequalities for certain minimal surfaces of the unit ball. Fraser won...

recompensed but I am still grateful to Hitler". Chebyshev function Isoperimetric inequality Low-rank approximation List of Baltic German scientists Erhard...

Young, L. C. (1959b), "Partial area. Part III: Symmetrization and the isoperimetric and least area problems" (PDF), Rivista di Matematica della Università...

A Theory of Cross-Spaces Robert Schatten 1950 153 LCCN 50-14439 27 Isoperimetric Inequalities in Mathematical Physics. G. Pólya, G. Szegö 1951 279 978-0691079882...

connectivity also relates to other connectivity attributes, such as the isoperimetric number, which is bounded below by half the algebraic connectivity. The...

functions not reducible to one-point extensions and solved the reverse isoperimetric problem. He produced a sharp version of the Banach-Steinhaus Theorem...

along the surface. A curve of constant U or constant V is known as an isoperimetric curve, or U (V) line. In CAD systems, surfaces are often displayed with...

identical. Ball used this inequality to estimate volume ratios and isoperimetric quotients for convex sets in and. There is also a geometric version...

2008, pp. 402–403, Lemma 18.1. Monterde, J.; Ongay, F. (2012), "An isoperimetric type problem for primitive Pythagorean hodograph curves", Computer Aided...

JSTOR 2974378. Weaver, James H. (1916). "Some theorems from Pappus on isoperimetric figures". School Science and Mathematics. 16 (8): 674–679. doi:10.1111/j...

Circle Packings of and Ambo Operations on Two Pentagonal Isoperimetric 2-dual-uniform tilings. C[33.42; 32.4.3.4]1 a33.42; 32.4.3.4]1 C[33.42; 32.4.3...

162 (2005) Fusco, N.; Maggi, F.; Pratelli, A. "The sharp quantitative isoperimetric inequality" Annals of Mathematics (2) 168 (2008) "NICOLA FUSCO". Wpage...

Retrieved 10 May 2016. Apostol, Tom; Mnatsakanian, Mamikon (2004). "Isoperimetric and Isoparametric Problems". Amer. Math. Monthly. 111 (2): 118–136....

Betweenness centrality Fractional chromatic number Algebraic connectivity Isoperimetric number Estrada index Strength Degree sequence Graph spectrum Characteristic...

Cyclic Sum Constant". MathWorld. Nowosad, Pedro (September 1968). "Isoperimetric eigenvalue problems in algebras". Communications on Pure and Applied...

(Formanek, Procesi, 1992); For n ≥ 3 {\displaystyle n\geq 3} , the isoperimetric function of O u t ( F n ) {\displaystyle \mathrm {Out} (F_{n})} is exponential...

the general form of Crofton formula. Blaschke–Lebesgue theorem and isoperimetric inequality, bounding the areas of curves of constant width Lay, Steven...

Grushko theorem (group theory) Higman's embedding theorem (group theory) Isoperimetric gap (geometric group theory, metric geometry) Jordan–Hölder theorem...

furthermore he writes that at the Meeting Baiada read the paper "An Isoperimetric Problem for Ship-Bodies" (Hollcroft 1950, pp. 161), presented by C....

Isamar Rosa; Shah, Niralee; Vieira, Luis Sordo; Wikner, Elena (2012), "Isoperimetric pentagonal tilings", Notices of the American Mathematical Society, 59...

2008-07-25 at the Wayback Machine [21] Leo Grady and Eric L. Schwartz. Isoperimetric graph partitioning for data clustering and image segmentation. IEEE...

next year a historical treatise on the calculus of variations and isoperimetrical problems. He next produced an astronomy; of which the first book (usually...

4310/jdg/1214509283 P. Papasoglu, Cheeger constants of surfaces and isoperimetric inequalities, Trans. Amer. Math. Soc. 361 (2009) 5139–5162. Burago,...

(Gersten, 1994). However, all free-by-cyclic groups satisfy a quadratic isoperimetric inequality (Bridson and Groves, 2010). All free-by-cyclic groups where...

graphometer, hexameter, hygrometer, hygrometry, isodiametric, isometric, isoperimetric, meter, metre, metric, metrology, metronome, monosymmetric, parameter...

applications to quasiregular mappings on manifolds; applications of isoperimetric methods to the Phragmén–Lindelöf principle for quasiregular mappings...

Rosa; Shah, Nirlee; Vieira, Luis Sordo; Wikner, Elena (2012-05-01), "Isoperimetric Pentagonal Tilings", Notices of the American Mathematical Society, 59...

W. Dauben (ed.). "Adrianus Romanus and Giovanni Camillo Glorioso on isoperimetric figures". Mathematical Perspectives. New York: 8. ISBN 9781483262574...

Differentialgeometrie I. Berlin: Springer-Verlag. Kazdan, Jerry L. (1982). "An isoperimetric inequality and Wiedersehen manifolds". Seminar on Differential Geometry...

For smooth functions, this can be understood as an application of the isoperimetric inequality to the function's level sets. In one dimension, this is Wirtinger's...

Hayman, Walter K. (1993), "A problem on Fourier series arising from an Isoperimetric inequality", in Ricci, Paolo Emilio (ed.), Problemi attuali dell'analisi...

in particular the discovery of the equivalence between Sobolev and isoperimetric/isocapacitary inequalities (1960), his counterexamples related to Hilbert's...

ISBN 978-1-4613-9732-8. ISSN 0940-4740. Gersten, S.M. (1993). "Isoperimetric and isodiametric functions of finite presentations". Geometric group...

almost flat manifolds, Astérisque 1981, Nr. 81, p. 148 "A note on the isoperimetric constant." In Annales scientifiques de l'École Normale Supérieure, vol...

Convex Body and an Improved Volume Algorithm (with Lovász László, 1993) Isoperimetric Problems for Convex Bodies and a Localization Lemma (coauthor, 1995)...

Gauss–Markov process Gaussian process Gaussian random field Gaussian isoperimetric inequality Large deviations of Gaussian random functions Girsanov's...

Demetres; Ellis, David; Keevash, Peter (2013), "An Approximate Vertex-Isoperimetric Inequality for $r$-sets", The Electronic Journal of Combinatorics, 4...

gave some complete sets of first order axioms, called Tarski's axioms. Isoperimetric inequality. For three dimensions it states that the shape enclosing...

W. Dauben (ed.). "Adrianus Romanus and Giovanni Camillo Glorioso on isoperimetric figures". Mathematical Perspectives. New York: 1–11. ISBN 9781483262574...

dimensions Shiing-Shen Chern, Finsler geometry Richard S. Hamilton, An isoperimetric estimate for the curve-shrinking flow Vaughan Jones, Loop groups and...

Banchoff, Thomas F.; Pohl, William F. (1971). "A generalization of the isoperimetric inequality". Journal of Differential Geometry. 6 (2): 175–192. doi:10...

8–11. Mossinghoff, Michael J. (2011), "Enumerating isodiametric and isoperimetric polygons", Journal of Combinatorial Theory, Series A, 118 (6): 1801–1815...

dmlcz/100949. MR 0266791. Harper, L. H. (1966). "Optimal numberings and isoperimetric problems on graphs". Journal of Combinatorial Theory. 1: 385–393. doi:10...

of mathematics, general editor (1962) William Karush, Oscar Tarcov Isoperimetric problems & index theorems (1942), William Karush, Thesis (Ph.D.) University...

manifolds. The Cartan–Hadamard conjecture states that the classical isoperimetric inequality should hold in all simply connected spaces of non-positive...

hyperbolic ones, corresponding to the hyperbolic plane). Connections to isoperimetric inequalities Milnor J. (1968). "A note on curvature and fundamental...

Columbia Electronic Encyclopedia, Sixth Edition at Answer.com. Pappus's Theorem at MathPages Pappus's work on the Isoperimetric Problem at Convergence...

)={\mbox{Volume}}(\Omega )={\mbox{const.}}} The answer, given by the isoperimetric inequality, is a ball. Find the shape of an airplane wing which minimizes...

on lower bounds on mixing time based on the "bottleneck ratio" and isoperimetric number, the next two chapters of the first part cover two important...

of this theorem used the invariance principle in conjunction with an isoperimetric theorem of Borell in Gaussian space; since then more direct proofs were...

later characterized relative hyperbolicity in terms of relative linear isoperimetric inequalities. Druțu and Sapir gave a characterization in terms of asymptotic...

Yang, Deane; Zhang, Gaoyong (2000), " L p {\displaystyle L_{p}} affine isoperimetric inequalities", Journal of Differential Geometry, 56 (1): 111–132, doi:10...

T, using the arithmetic-geometric mean inequality, is obtained the isoperimetric inequality for triangles: T ≤ 3 36 ( a + b + c ) 2 = 3 9 s 2 {\displaystyle...

Hayman, Walter K. (1993), "A problem on Fourier series arising from an Isoperimetric inequality", in Ricci, Paolo Emilio (ed.), Problemi attuali dell'analisi...