Barycentric stability of nonlocal perimeters: the convex case

TL;DR

This paper proves a sharp nonlocal isoperimetric inequality for convex sets, extending Fuglede's classical result to a nonlocal context with barycentric asymmetry.

Contribution

It introduces a nonlocal quantitative isoperimetric inequality involving barycentric asymmetry for convex sets, providing a nonlocal analogue of Fuglede's 1993 result.

Findings

Established a sharp nonlocal isoperimetric inequality for convex sets

Extended Fuglede's classical isoperimetric result to a nonlocal setting

Linked barycentric asymmetry with nonlocal perimeter stability

Abstract

In this work, we establish a sharp form of a nonlocal quantitative isoperimetric inequality involving the barycentric asymmetry for convex sets. This result can be seen as the nonlocal analogue of the one obtained by Fuglede in 1993.