Isoperimetric problems for a nonlocal perimeter of Minkowski type

TL;DR

This paper establishes a quantitative isoperimetric inequality for a nonlocal Minkowski-type perimeter and explores the shape and existence of minimizers in related problems with convexity constraints.

Contribution

It provides the first quantitative inequality for a nonlocal Minkowski perimeter and analyzes minimizers in isoperimetric problems with repulsive interactions.

Findings

Proved a quantitative isoperimetric inequality for nonlocal Minkowski perimeter.

Established existence and characterized minimizers under convexity constraints.

Described the shape of minimizers in specific parameter regimes.

Abstract

We prove a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under convexity constraints. We show existence of minimizers, and we describe the shape of minimizers in certain parameter regimes.