Rigidity and stability of Caffarelli's log-concave perturbation theorem

Guido De Philippis, Alessio Figalli

Research output: Contribution to journalArticlepeer-review


In this note we establish some rigidity and stability results for Caffarelli's log-concave perturbation theorem. As an application we show that if a 1-log-concave measure has almost the same Poincaré constant as the Gaussian measure, then it almost splits off a Gaussian factor.

Original languageEnglish (US)
Pages (from-to)59-70
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
StatePublished - May 1 2017


  • Log Concave measures
  • Optimal transport

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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