A stability inequality for the planar lens partition
Analysis of PDEs
2025-01-28 v2
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.
Cite
@article{arxiv.2407.21677,
title = {A stability inequality for the planar lens partition},
author = {Marco Bonacini and Riccardo Cristoferi and Ihsan Topaloglu},
journal= {arXiv preprint arXiv:2407.21677},
year = {2025}
}
Comments
This is a post-peer-review, pre-copyedit version of an article published in Proceedings of the Royal Society of Edinburgh: Section A Mathematics. The final authenticated version is available online at: https://doi.org/10.1017/prm.2025.2