In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n {\displaystyle n} -dimensional...

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...

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

two-dimensional surface Circumgon – Geometric figure which circumscribes a circle Isoperimetric inequality – Geometric inequality which sets a lower bound on the surface...

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"...

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

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

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...

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...

{\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...

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...

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

(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...

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

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

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

Academic Chair. His research focuses on analysis and geometry, including isoperimetric inequalities, curvature-dimension conditions, convex geometry, and concentration...

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

Byrsa ("hide"). (This event is commemorated in modern mathematics: The "isoperimetric problem" of enclosing the maximum area within a fixed boundary is often...

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...

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...

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

multiplicity ( n k ) {\displaystyle {\binom {n}{k}}} in both cases. has isoperimetric number h(G) = 1. The family Qn for all n > 1 is a Lévy family of graphs...

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

relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality. In an x–y Cartesian coordinate system, the circle with centre...

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

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

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

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