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 by figalli on 19 Aug 2024

[BibTeX]

Published Paper

Inserted: 31 may 2016
Last Updated: 19 aug 2024

Journal: Nonlinear Anal.
Year: 2017

ArXiv: 1605.09702 PDF

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.


Download: