Results 41 to 50 of about 1,372 (214)
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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on some discrete Bonnesen-style isoperimetric inequalities
, 2023 This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on Schur convex function are established.
Dong, Xu, Zeng, Chunna
core
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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Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel [PDF]
Opuscula MathematicaWe deduce isoperimetric estimates for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable
Gonzalo Galiano
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On Non Local p-Laplacian with Right Hand Side Radon Measure
Fractal and Fractional, 2022 The aim of this paper is to investigate the following non local p-Laplacian problem with data a bounded Radon measure ϑ∈Mb(Ω): (−Δ)psu=ϑinΩ, with vanishing conditions outside Ω, and where s∈(0,1),2 ...
Mohammed Kbiri Alaoui
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On A. Hurwitz’ method in isoperimetric inequalities [PDF]
Proceedings of the American Mathematical Society, 1978 We show that if M is complete simply connected with nonpositive sectional curvatures, Ω
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A strong quantitative form of the fractional isoperimetric inequality
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of oscillation of the boundary. This generalizes the local result by Fusco and Julin in [22].
Eleonora Cinti +2 more
wiley +1 more source
Reifenberg’s isoperimetric inequality revisited [PDF]
Calculus of Variations and Partial Differential Equations, 2019 We prove a generalization of Reifenberg's isoperimetric inequality. The main result of this paper is used to establish existence of a minimizer for an anisotropically-weighted area functional among a collection of surfaces which satisfies a set of axioms, namely being closed under certain deformations and Hausdorff limits.
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In‐and‐Out: Algorithmic Diffusion for Sampling Convex Bodies
Random Structures &Algorithms, Volume 68, Issue 3, May 2026.ABSTRACT We present a new random walk for uniformly sampling high‐dimensional convex bodies. It achieves state‐of‐the‐art runtime complexity with stronger guarantees on the output than previously known, namely in Rényi divergence (which implies TV, 𝒲2, KL, χ2$$ {\chi}^2 $$).
Yunbum Kook +2 more
wiley +1 more source
Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, Volume 79, Issue 4, Page 1012-1072, April 2026.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
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