Results 51 to 60 of about 469,360 (206)
A Discrete Isoperimetric Inequality on Lattices [PDF]
Discrete & Computational Geometry, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
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
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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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Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
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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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Isoperimetric Inequalities for Convex Cones [PDF]
Proceedings of the American Mathematical Society, 1990 We present here an isoperimetric inequality for sets contained in a convex cone. Some applications to symmetrization problems and Sobolev inequalities are also indicated.
LIONS P. L., PACELLA, Filomena
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Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 762-822, March 2026.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
wiley +1 more source
Exact bounds for tail probabilities of martingales with bounded differences
Lietuvos Matematikos Rinkinys, 2009 We consider random walks, say Wn = {0, M1, . . ., Mn} of length n starting at 0 and based on a martingale sequence Mk = X1 + ··· + Xk with differences Xm. Assuming |Xk| \leq 1 we solve the isoperimetric problem Bn(x) = supP\{Wn visits an interval [x,∞
Dainius Dzindzalieta
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Isoperimetric inequalities in graphs and surfaces [PDF]
Electronic Notes in Discrete Mathematics, 2014 Let M be the set of metric spaces that are either graphs with bounded degree or Riemannian manifolds with bounded geometry. Kanai proved the quasi-isometric stability of several geometric properties (in particular, of isoperimetric inequalities) for the spaces in M.
Cantón Pire, Alicia +3 more
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