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.
Rigidity and stability of Caffarelli's log-concave perturbation theorem / De Philippis, Guido; Figalli, Alessio. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 154:(2017), pp. 59-70. [10.1016/j.na.2016.10.006]
Rigidity and stability of Caffarelli's log-concave perturbation theorem
De Philippis, Guido;
2017-01-01
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.File in questo prodotto:
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