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.
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