Rigidity and stability of Caffarelli's log-concave perturbation theorem. (May 2017)

• Record Type: Journal Article
• Authors: De Philippis, Guido; Figalli, Alessio
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 59
• Page End: 70
• Publication Date: 2017-05
• Subjects: Optimal transport -- Log Concave measures; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.10.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.