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Essential connectedness and the rigidity problem for Gaussian symmetrization

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arxiv 1304.4527 v1 pith:GSQMD6MU submitted 2013-04-16 math.AP

Filippo Cagnetti , Maria Colombo , Guido De Philippis , Francesco Maggi This is my paper
classification math.AP
keywords connectednessgaussianrigiditysymmetrizationborelcasescharacterizationcondition
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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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