Calculus of Variations and Geometric Measure Theory
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G. De Philippis - A. Figalli

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

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


Accepted Paper

Inserted: 31 may 2016
Last Updated: 10 oct 2016

Journal: Nonlinear Anal.
Year: 2016


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.


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