Rigidity of equality cases in steiner's perimeter inequality

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

Research output: Contribution to journalArticlepeer-review


Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to a hyperplane.

Original languageEnglish (US)
Pages (from-to)1535-1593
Number of pages59
JournalAnalysis and PDE
Issue number7
StatePublished - 2014


  • Equality cases
  • Rigidity
  • Symmetrization

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics


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