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

created by dephilipp on 31 May 2016
modified on 10 Oct 2016

[BibTeX]

Accepted Paper

Inserted: 31 may 2016
Last Updated: 10 oct 2016

Journal: Nonlinear Anal.
Year: 2016

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