Calculus of Variations and Geometric Measure Theory

F. Cagnetti - M. Perugini - D. Stöger

Rigidity for perimeter inequality under spherical symmetrisation

created by cagnetti on 13 Aug 2019
modified by perugini on 22 Oct 2021


Published Paper

Inserted: 13 aug 2019
Last Updated: 22 oct 2021

Journal: Calc. Var. Partial Differential Equations
Year: 2019


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.