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

Guido De Philippis; Alessio Figalli

doi:10.1016/j.na.2016.10.006

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

Guido De Philippis, Alessio Figalli

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	59-70
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	154
DOIs	https://doi.org/10.1016/j.na.2016.10.006
State	Published - May 1 2017

Keywords

Log Concave measures
Optimal transport

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2016.10.006

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title = "Rigidity and stability of Caffarelli's log-concave perturbation theorem",

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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author = "{De Philippis}, Guido and Alessio Figalli",

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AU - De Philippis, Guido

AU - Figalli, Alessio

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N2 - 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.

AB - 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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KW - Optimal transport

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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