posted on 2023-06-08, 18:47authored byFilippo 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.