In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n {\displaystyle n} -dimensional...
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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...
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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...
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In geometry, the isoperimetric point is a triangle center — a special point associated with a plane triangle. The term was originally introduced by G...
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two-dimensional surface Circumgon – Geometric figure which circumscribes a circle Isoperimetric inequality – Geometric inequality which sets a lower bound on the surface...
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Cheeger constant (graph theory) (redirect from Isoperimetric number)
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"...
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Dehn function (redirect from Isoperimetric function)
notion of a Dehn function is motivated by isoperimetric problems in geometry, such as the classic isoperimetric inequality for the Euclidean plane and,...
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In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov, and later independently by Christer Borell, states...
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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...
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Area of a circle (section Isoperimetric inequality)
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...
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{\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...
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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...
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William (1894). "Isoperimetrical problems". Nature Series: Popular Lectures and Addresses. II: 571–592. Chavel, Isaac (2001). Isoperimetric inequalities....
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(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...
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inequality is a functional isoperimetric inequality for the canonical Gaussian measure. It generalizes the Gaussian isoperimetric inequality. The equation...
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theory field of mathematics, Talagrand's concentration inequality is an isoperimetric-type inequality for product probability spaces. It was first proved...
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restating the problem as a minimization of the Rayleigh quotient. The isoperimetric inequality can be deduced from the Pólya–Szegő inequality with p = 1...
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Academic Chair. His research focuses on analysis and geometry, including isoperimetric inequalities, curvature-dimension conditions, convex geometry, and concentration...
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it satisfies a linear isoperimetric inequality. Moreover, there is an isoperimetric gap in the possible spectrum of isoperimetric functions for finitely...
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Byrsa ("hide"). (This event is commemorated in modern mathematics: The "isoperimetric problem" of enclosing the maximum area within a fixed boundary is often...
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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...
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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...
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terms of the length. Mikhail Gromov once voiced the opinion that the isoperimetric inequality was known already to the Ancient Greeks. The mythological...
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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...
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Bonnesen's inequality (redirect from Isoperimetric defect)
circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality. More precisely, consider a planar simple closed curve of...
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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...
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SDE which has a weak solution but no strong solution. The Gaussian isoperimetric inequality (proved by Vladimir Sudakov and Tsirelson, and independently...
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linear isoperimetric inequality; it turns out that having such an isoperimetric inequality characterises Gromov-hyperbolic spaces. Linear isoperimetric inequalities...
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elliptic equations and reaction-diffusion equations, and for her book on isoperimetric inequalities. She is a professor emerita of mathematics at the University...
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Gerrymandering (section Minimum isoperimetric quotient)
subdivisions, such as neighborhoods or voting districts (something isoperimetric rules would discourage); and it allows concave coastline districts,...
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