Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. Figalli

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

created by dephilipp on 31 May 2016
modified on 30 Oct 2017


Accepted Paper

Inserted: 31 may 2016
Last Updated: 30 oct 2017

Journal: Nonlinear Anal.
Year: 2016

ArXiv: 1605.09702 PDF


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 Poincar\'e constant as the Gaussian measure, then it almost splits off a Gaussian factor.