Published Paper

Inserted: 31 jul 2024
Last Updated: 27 jan 2025

Journal: Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Year: 2025
Doi: https://doi.org/10.1017/prm.2025.2

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.

Download:

• lens_fin.pdf