Results 21 to 30 of about 308 (179)
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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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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Notices of the American Mathematical SocietyThe isoperimetric problem is one of the oldest and most famous problems in geometry.
Eichmair, Michael, Brendle, Simon
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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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Log-Minkowski inequalities for the Lp $L_{p}$-mixed quermassintegrals
Journal of Inequalities and Applications, 2019 Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies. Recently, Stancu proved the log-Minkowski inequality for mixed volumes; Wang, Xu, and Zhou gave the Lp $L_{p ...
Chao Li, Weidong Wang
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On Isoperimetric Inequalities in Minkowski Spaces
Journal of Inequalities and Applications, 2010 The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces).
Horst Martini, Zokhrab Mustafaev
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Dual Orlicz geominimal surface area
Journal of Inequalities and Applications, 2016 The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski ...
Tongyi Ma, Weidong Wang
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