Essential connectedness and the rigidity problem for Gaussian symmetrization

Filippo Cagnetti; Maria Colombo; Guido De Philippis; Francesco Maggi

doi:10.4171/JEMS/669

Essential connectedness and the rigidity problem for Gaussian symmetrization

Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi

Mathematics

Research output: Contribution to journal › Article › peer-review

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, and of possible broader interest.

Original language	English (US)
Pages (from-to)	395-439
Number of pages	45
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/669
State	Published - 2017

Keywords

Equality cases
Gauss space
Rigidity
Symmetrization

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/JEMS/669

Cite this

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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, and of possible broader interest.",

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AU - Colombo, Maria

AU - De Philippis, Guido

AU - Maggi, Francesco

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KW - Symmetrization

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Essential connectedness and the rigidity problem for Gaussian symmetrization

Abstract

Keywords

ASJC Scopus subject areas

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