JournalsjemsVol. 19, No. 2pp. 395–439

Essential connectedness and the rigidity problem for Gaussian symmetrization

  • Filippo Cagnetti

    University of Sussex, Brighton, UK
  • Maria Colombo

    Scuola Normale Superiore, Pisa, Italy
  • Guido De Philippis

    University of Bonn, Germany
  • Francesco Maggi

    The University of Texas at Austin, USA
Essential connectedness and the rigidity problem for Gaussian symmetrization cover

A subscription is required to access this article.

Abstract

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.

Cite this article

Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi, Essential connectedness and the rigidity problem for Gaussian symmetrization. J. Eur. Math. Soc. 19 (2017), no. 2, pp. 395–439

DOI 10.4171/JEMS/669