Results 21 to 30 of about 13,857 (195)
Sharp isoperimetric inequalities via the ABP [PDF]
, 2016 Given an arbitrary convex cone of Rn, we find a geometric class of homogeneous weights for which balls centered at the origin and intersected with the cone are minimizers of the weighted isoperimetric problem in the convex cone.
Cabré Vilagut, Xavier +2 more
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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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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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Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey [PDF]
, 2017 This paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate.
Cabré Vilagut, Xavier
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An Asymptotic Isoperimetric Inequality [PDF]
Geometric And Functional Analysis, 1998 For a finite metric space \(V\) with a metric \(\rho\) and probability measure \(\mu\), let \(V^n\) be the product metric space in which the distance between \(a= (a_1,\dots, a_n)\) and \(b= (b_1,\dots, b_n)\) is \(\rho_n(a,b)= \sum_i\rho(a_i, b_i)\) and the measure \(\mu_n(a_1,\dots, a_n)= \prod_i\mu(a_i)\). For any \(d\geq 0\) the \(d\)-neighbourhood
Alon, N., Boppana, R., Spencer, J.
openaire +2 more sources
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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Quantitative isoperimetric inequalities for log-convex probability measures on the line
, 2014 The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of ...
Feo, F., Posteraro, M. R., Roberto, C.
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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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A strong form of the Quantitative Isoperimetric inequality
, 2011 We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the ...
A Figalli +8 more
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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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