Rigidity for perimeter inequality under spherical symmetrisation
Analysis of PDEs
2020-05-04 v2
Abstract
Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogonal transformations) of the extremals is provided. This is obtained through a careful analysis of the equality cases, and studying fine properties of the circular symmetrisation, which was firstly introduced by P\'olya in 1950.
Cite
@article{arxiv.1908.04865,
title = {Rigidity for perimeter inequality under spherical symmetrisation},
author = {Filippo Cagnetti and Matteo Perugini and Dominik Stöger},
journal= {arXiv preprint arXiv:1908.04865},
year = {2020}
}
Comments
48 pages