Rigidity for perimeter inequality under spherical symmetrisation
arXiv:1908.04865
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 Pólya in 1950.
48 pages