We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federer's definition of indecomposable current.

Essential connectedness and the rigidity problem for Gaussian symmetrization / Cagnetti, F.; Colombo, M.; De Philippis, Guido; Maggi, F.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 19:2(2017), pp. 395-439. [10.4171/JEMS/669]

Essential connectedness and the rigidity problem for Gaussian symmetrization

De Philippis, Guido;
2017

Abstract

We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federer's definition of indecomposable current.
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439
https://arxiv.org/abs/1304.4527
Cagnetti, F.; Colombo, M.; De Philippis, Guido; Maggi, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/60745
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