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

against those of the Euclidean space). In the Euclidean space, the isoperimetric inequality says that of all bodies with the same volume, the ball has the...

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

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

proof of the isoperimetric inequality for curves in the plane. A variety of closely related results are today known as Wirtinger's inequality, all of which...

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

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

The Sobolev inequality is equivalent to the isoperimetric inequality (in any dimension), with the same best constants. Wirtinger's inequality also generalizes...

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...

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

an application of the isoperimetric inequality to the function's level sets. In one dimension, this is Wirtinger's inequality for functions. However...

Bobkov's inequality is a functional isoperimetric inequality for the canonical Gaussian measure. It generalizes the Gaussian isoperimetric inequality. The...

Hoory, Linial & Wigderson (2006) J.Dodziuk, Difference Equations, Isoperimetric inequality and Transience of Certain Random Walks, Trans. Amer. Math. Soc...

of the length. Mikhail Gromov once voiced the opinion that the isoperimetric inequality was known already to the Ancient Greeks. The mythological tale...

Hitchin–Thorpe inequality Isoperimetric inequality Jordan's inequality Jung's theorem Loewner's torus inequality Łojasiewicz inequality Loomis–Whitney inequality Melchior's...

p} are related by the isoperimetric inequality p 2 > 12 3 T . {\displaystyle p^{2}>12{\sqrt {3}}T.} This is a strict inequality for isosceles triangles...

However, the inequality goes in the opposite direction. Thus, Pu's inequality can be thought of as an "opposite" isoperimetric inequality. Filling area...

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

The Pólya–Szegő inequality can be proved by combining the coarea formula, Hölder’s inequality and the classical isoperimetric inequality. If the function...

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

similarity transformations of the curve. According to the isoperimetric inequality, the isoperimetric ratio has its minimum value, 4π, for a circle; any other...

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

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...

volume ratios and isoperimetric quotients for convex sets in and. There is also a geometric version of the more general inequality in which the maps B...

integer lattice. Isoperimetric inequality Milman's reverse Brunn–Minkowski inequality Minkowski–Steiner formula Prékopa–Leindler inequality Vitale's random...

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,...

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

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 simple...

More generally, the Faber–Krahn inequality holds in any Riemannian manifold in which the isoperimetric inequality holds. In particular, according to...