Results 31 to 40 of about 308 (179)

Functional Geominimal Surface Area and Its Related Affine Isoperimetric Inequality

Journal of Function Spaces, 2020
The first variation of the total mass of log-concave functions was studied by Colesanti and Fragalà, which includes the Lp mixed volume of convex bodies. Using Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log-
Niufa Fang, Jin Yang
doaj   +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.
openaire   +2 more sources

On the deterministic interior body of random polytopes

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract Let {Xi}i=1∞$\lbrace X_i\rbrace _{i=1}^{\infty }$ be a sequence of independent copies of a random vector X$X$ in Rn$\mathbb {R}^n$. We revisit the question to determine the asymptotic shape of the random polytope KN=conv{X1,…,XN}$K_N={\rm conv}\lbrace X_1,\ldots,X_N\rbrace$ where N>n$N>n$.
Minas Pafis, Natalia Tziotziou
wiley   +1 more source

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
openaire   +1 more source

Qualitative properties of solutions to parabolic anisotropic equations, part II — The anisotropic Trudinger's equation

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We study the local regularity properties of weak solutions to a special class of anisotropic doubly nonlinear parabolic operators, whose prototype is the anisotropic Trudinger's equation ut−∑i=1NDiu2−pi|Diu|pi−2Diu=0,u⩾0.$$\begin{equation*} u_t- \sum \limits _{i=1}^N D_i{\left(u^{2-p_i}|D_i u|^{p_i-2} D_i u\right)}=0,\qquad u\geqslant 0.
S. Ciani, E. Henriques, M. O. Savchenko, I. I. Skrypnik   +3 more
wiley   +1 more source

Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions

Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.
Abstract Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain Ω⊂Rd$\Omega \subset \mathbb {R}^d$ with d⩾3$d\geqslant 3$, we consider the Robin–Laplacian torsional rigidity τα(Ω)$\tau _\alpha (\Omega)$ with negative boundary parameter α$\alpha$ and we show that sharp inequalities for τα(Ω)$\tau _\alpha (\Omega)$ hold if ...
Nunzia Gavitone, David Krejčiřík, Gloria Paoli   +2 more
wiley   +1 more source

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, Enzo Maria Merlino, Berardo Ruffini   +2 more
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
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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, Santosh S. Vempala, Matthew S. Zhang   +2 more
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