A stability inequality for the planar lens partition

TL;DR

This paper establishes a sharp stability inequality for the standard lens partition in the plane, strengthening its local minimality and applying the result to a nonlocal isoperimetric perturbation.

Contribution

It provides a quantitative stability inequality for the planar lens partition, enhancing understanding of its minimality properties.

Findings

Proves a sharp stability inequality for the standard lens partition.

Strengthens the local minimality of the lens partition in a quantitative manner.

Applies the stability result to a nonlocal perturbation of an isoperimetric problem.

Abstract

Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens; hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem.