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Essential connectedness and the rigidity problem for Gaussian symmetrization

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posted on 2023-06-08, 18:47 authored by Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of the European Mathematical Society

ISSN

1435-9855

Publisher

European Mathematical Society

Issue

2

Volume

19

Page range

395-439

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2014-10-24

First Open Access (FOA) Date

2017-03-13

First Compliant Deposit (FCD) Date

2016-01-13

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