Essential connectedness and the rigidity problem for Gaussian symmetrization
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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