Results 51 to 60 of about 13,857 (195)
Stability of reverse isoperimetric inequalities in the plane: Area, Cheeger, and inradius
Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.Abstract In this paper, we present stability results for various reverse isoperimetric problems in R2$\mathbb {R}^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for λ$\lambda$‐convex bodies — convex bodies with the property that each of their boundary points p$p$ supports a ball of radius 1/λ$1/\lambda$ so that the ...
Kostiantyn Drach, Kateryna Tatarko
wiley +1 more source
Equivalence of Some Affine Isoperimetric Inequalities
Journal of Inequalities and Applications, 2009 We establish the equivalence of some affine isoperimetric inequalities which include the -Petty projection inequality, the -Busemann-Petty centroid inequality, the "dual" -Petty projection inequality, and the "dual" -Busemann-Petty inequality.
Yu Wuyang
doaj
Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower Bound
, 2009 It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the ...
Milman, Emanuel
core +2 more sources
Pólya's conjecture for Dirichlet eigenvalues of annuli
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques and a rigorous computer‐assisted analysis. As
Nikolay Filonov +3 more
wiley +1 more source
An optimal relative isoperimetric inequality in concave cylindrical domains in
Journal of Inequalities and Applications, 2000 We prove an optimal relative isoperimetric inequality in concave cylindrical domains in , which generalizes the well-known two-dimensional relative isoperimetric inequality in a planar sector with angle greater than or equal to .
Kim Inho
doaj
Geodesics in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2015 We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from ...
Hajłasz Piotr, Zimmerman Scott
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Counting Independent Sets in Percolated Graphs via the Ising Model
Random Structures &Algorithms, Volume 68, Issue 1, January 2026.ABSTRACT Given a graph G$$ G $$, we form a random subgraph Gp$$ {G}_p $$ by including each edge of G$$ G $$ independently with probability p$$ p $$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite graphs satisfying certain vertex‐isoperimetric properties, extending the work of ...
Anna Geisler +3 more
wiley +1 more source
On the structure of subsets of the discrete cube with small edge boundary
Discrete Analysis, 2018 On the structure of subsets of the discrete cube with small edge boundary, Discrete Analysis 2018:9, 29 pp. An isoperimetric inequality is a statement that tells us how small the boundary of a set can be given the size of the set, for suitable notions ...
David Ellis +2 more
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Inequalities and counterexamples for functional intrinsic volumes and beyond
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract We show that analytic analogs of Brunn–Minkowski‐type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and Saorín Gómez.
Fabian Mussnig, Jacopo Ulivelli
wiley +1 more source
The sharp quantitative isoperimetric inequality [PDF]
Annals of Mathematics, 2008 The isoperimetric inequality states that for any Borel set \(E\subset{\mathbb R}^n\), \(n\geq 2\), with finite Lebesgue measure \(|E|\) it holds \(P(E)\geq n\omega_n^{1/n}|E|^{(n-1)/n}\), with equality if and only if \(E\) is a ball. Here \(P\) denotes the (distributional) perimeter and \(\omega_n\) is the measure of the unit ball \(B\subset{\mathbb R}^
FUSCO, NICOLA, MAGGI F., PRATELLI A.
openaire +7 more sources