Inserted: 16 apr 2013
Last Updated: 21 oct 2014
Journal: J. Eur. Math. Soc.
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.
Keywords: Geometric measure theory, Gauss space, Symmetrization