English

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

R2 v1 2026-06-23T10:46:52.298Z