Calculus of Variations and Geometric Measure Theory

F. Cagnetti - M. Colombo - G. De Philippis - F. Maggi

Essential connectedness and the rigidity problem for Gaussian symmetrization

created by maggi on 16 Apr 2013
modified by dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 16 apr 2013
Last Updated: 30 oct 2017

Journal: J. Eur. Math. Soc.
Year: 2013

ArXiv: 1304.4527 PDF


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