Essential connectedness and the rigidity problem for Gaussian symmetrization

Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)395-439
Number of pages45
JournalJournal of the European Mathematical Society
Issue number2
StatePublished - 2017


  • Equality cases
  • Gauss space
  • Rigidity
  • Symmetrization

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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