Published Paper
Inserted: 13 aug 2019
Last Updated: 22 oct 2021
Journal: Calc. Var. Partial Differential Equations
Year: 2019
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.
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