Calculus of Variations and Geometric Measure Theory
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F. Cagnetti - M. Perugini - D. Stöger

Rigidity for perimeter inequality under spherical symmetrisation

created by cagnetti on 13 Aug 2019
modified on 07 Jun 2020


Accepted Paper

Inserted: 13 aug 2019
Last Updated: 7 jun 2020

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.


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