Results 21 to 30 of about 469,360 (206)
Randomized Isoperimetric Inequalities [PDF]
, 2017 We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities admit stronger randomized forms in the following sense: for natural families of associated random convex sets one has ...
Paouris, Grigoris, Pivovarov, Peter
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An Isoperimetric Inequality for Planar Triangulations [PDF]
Discrete & Computational Geometry, 2017 We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.
Omer Angel, Itai Benjamini, Nizan Horesh
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Thermodynamic instabilities of generalized exotic BTZ black holes
Journal of High Energy Physics, 2019 We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume C V [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black ...
Wan Cong, Robert B. Mann
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Relative Isoperimetric Inequality for Minimal Submanifolds in a Riemannian Manifold
Journal of Inequalities and Applications, 2010 Let Σ be a domain on an m-dimensional minimal submanifold in the outside of a convex set C in 𝕊n or ℍn. The modified volume M(Σ) is introduced by Choe and Gulliver (1992) and we prove a sharp modified relative isoperimetric
Juncheol Pyo
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A sharp relative isoperimetric inequality for the square
Comptes Rendus. Mathématique, 2021 We compute the exact value of the least “relative perimeter” of a shape $S$, with a given area, contained in a unit square; the relative perimeter of $S$ being the length of the boundary of $S$ that does not touch the border of the square.
Brezis, Haim, Bruckstein, Alfred
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Torsional rigidity on compact Riemannian manifolds with lower Ricci curvature bounds
Open Mathematics, 2015 In this article we prove a reverse Hölder inequality for the fundamental eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with lower Ricci curvature bounds.
Gamara Najoua +2 more
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Compressions and isoperimetric inequalities
Journal of Combinatorial Theory, Series A, 1991 Let \(G=(V,E)\) be a graph. For \(A\subset V\) and \(y\in V\), set \(D(A,y)=\inf \{d(x,y):\) \(x\in A\}\), where d is the usual graph metric. For \(t=0,1,2,...\), \(A_{(t)}=\{y\in V:\) d(A,y)\(\leq t\}\) is the t-boundary of A and \(A_{(1)}=\partial A\) is the boundary of A.
Béla Bollobás, Imre Leader
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Edge-Isoperimetric Inequalities and Influences [PDF]
Combinatorics, Probability and Computing, 2007 We give a combinatorial proof of the result of Kahn, Kalai and Linial [16], which states that every balanced boolean function on the n-dimensional boolean cube has a variable with influence of at least $\Omega\bigl(\frac{\log n}{n}\bigr)$ .
Dvir Falik, Alex Samorodnitsky
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An affine isoperimetric inequality for log-concave functions [PDF]
, 2023 The authors gave an affine isoperimetric inequality \cite{LYZ2010} that gives a lower bound for the volume of a polar body and the equality holds if and only if the body is a simplex.
Zhang, Zengle, Zhou, Jiazu
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LOW-DEGREE BOOLEAN FUNCTIONS ON $S_{n}$ , WITH AN APPLICATION TO ISOPERIMETRY
Forum of Mathematics, Sigma, 2017 We prove that Boolean functions on $S_{n}$ , whose Fourier transform is highly concentrated on irreducible representations indexed by partitions of
DAVID ELLIS, YUVAL FILMUS, EHUD FRIEDGUT
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