Essential connectedness and the rigidity problem for Gaussian symmetrization

Essential connectedness and the rigidity problem for Gaussian symmetrization

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 c...

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Bibliographic Details
Main Authors: Cagnetti, Filippo, Colombo, Maria, De Philippis, Guido, Maggi, Francesco
Format: Journal Article
Language:English
Published: 16-04-2013
Subjects:
Mathematics - Analysis of PDEs
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.1304.4527