Results 21 to 30 of about 520,398 (211)
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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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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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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A RELATIVE ISOPERIMETRIC INEQUALITY
Communications in Contemporary Mathematics, 2012 We prove that, if Ω is an open subset of ℝN with finite measure, there exists a hyperplane H through 0 such that the measure of Ω ∩ H is less than the measure of B ∩ H, where B is the open ball with center 0 having the same measure as Ω. An application is given to the optimal Poincaré inequality on BV(Ω).
Brock, Friedemann, Willem, Michel
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Isoperimetric inequalities in simplicial complexes [PDF]
Combinatorica, 2015 In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high ...
Ori Parzanchevski +2 more
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Bonnesen-style symmetric mixed inequalities
Journal of Inequalities and Applications, 2016 In this paper, we investigate the symmetric mixed isoperimetric deficit Δ 2 ( K 0 , K 1 ) $\Delta_{2}(K_{0},K_{1})$ of domains K 0 $K_{0}$ and K 1 $K_{1}$ in the Euclidean plane R 2 $\mathbb{R}^{2}$ .
Pengfu Wang, Miao Luo, Jiazu Zhou
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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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