Book ChapterDOI
Sets of Finite Perimeter and Geometric Variational Problems: SETS OF FINITE PERIMETER
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The article was published on 2012-01-01. It has received 208 citations till now. The article focuses on the topics: Perimeter.read more
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Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies
TL;DR: In this paper, a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform with respect to s bounded away from 0, was obtained for balls of small volume with a competition between perimeter and nonlocal potentials.
Journal ArticleDOI
A note on the Hanson-Wright inequality for random vectors with dependencies
TL;DR: In this paper, it was shown that quadratic forms in isotropic random vectors satisfy the Hanson-Wright inequality with constant k, where k is an absolute constant, thus eliminating the logarithmic factors in a recent estimate by Vu and Wang.
Journal ArticleDOI
Local and global minimality results for a nonlocal isoperimetric problem on R^N
TL;DR: It is shown that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the $L^1$-norm.
Journal ArticleDOI
Quantitative flatness results and $BV$-estimates for stable nonlocal minimal surfaces
TL;DR: In this paper, it was shown that a stable set in the plane with perimeter in the dimension of 2, 3 is a half-space in the Euclidean plane, with a universal bound on the measure of the symmetric difference.
Journal ArticleDOI
The quantitative isoperimetric inequality and related topics
TL;DR: In this article, the authors present some recent stability results concerning the isoperimetric inequality and other related geometric and functional inequalities, and the main techniques and approaches to this field are discussed.