Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024799 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 12 Pages |
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.
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Authors
Guido De Philippis, Alessio Figalli,