Results 41 to 50 of about 1,599 (218)
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
wiley +1 more source
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
wiley +1 more source
Exact Face-isoperimetric Inequalities
European Journal of Combinatorics, 1990 Let \([p]^ N\) be the grid, i.e. \([p]^ N=\{0,1,...,N-1\}\). The authors give the best possible upper bound for the number of faces of a fixed dimension contained in a subset of the grid. As a conjecture the result appeared in \textit{B. Bollobás} and \textit{A. J. Radcliffe} [Eur. J. Comb. 11, No.4, 323-333 (1990; see the review above)].
Béla Bollobás, Imre Leader
openaire +1 more source
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
A Discrete Isoperimetric Inequality on Lattices [PDF]
Discrete & Computational Geometry, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
The convex hull of a convex space curve with four vertices
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, that is, four points of vanishing torsion, and lying on the boundary of its convex hull. Moreover, we show that the upper bound is attained when the curve intersects every plane in at most four points, a condition studied by ...
Jakob Bohr +2 more
wiley +1 more source
Un nuovo approccio alle disuguaglianze isoperimetriche quantitative
Bruno Pini Mathematical Analysis Seminar, 2011 We introduce a new variational method for studying geometric and functional inequalities with quantitative terms. In the context of isoperimetric-type inequalities, this method (called Selection Principle) is based on a penalization technique combined ...
Gian Paolo Leonardi
doaj
Harmonic maps to the circle with higher dimensional singular set
Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.Abstract In a closed, oriented ambient manifold (Mn,g)$(M^n,g)$ we consider the problem of finding S1$\mathbb {S}^1$‐valued harmonic maps with prescribed singular set. We show that the boundary of any oriented (n−1)$(n-1)$‐submanifold can be realised as the singular set of an S1$\mathbb {S}^1$‐valued map, which is classically harmonic away from the ...
Marco Badran
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