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arXiv · 1304.4527

Essential connectedness and the rigidity problem for Gaussian symmetrization

Filippo Cagnetti·Maria Colombo·Guido De Philippis·Francesco Maggi
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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.

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Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi. 2013-04-16. Essential connectedness and the rigidity problem for Gaussian symmetrization. https://arxiv.org/abs/1304.4527

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