@article{d207536329d34f42a8d0af5682d64783,
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.",
keywords = "Log Concave measures, Optimal transport",
author = "{De Philippis}, Guido and Alessio Figalli",
note = "Funding Information: G.D.P. is supported by the MIUR SIR-grant “Geometric Variational Problems” (RBSI14RVEZ). G.D.P is a member of the “Gruppo Nazionale per l'Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni” (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). A.F. was partially supported by NSF Grants DMS-1262411 and DMS-1361122. Publisher Copyright: {\textcopyright} 2016 Elsevier Ltd",
year = "2017",
month = may,
day = "1",
doi = "10.1016/j.na.2016.10.006",
language = "English (US)",
volume = "154",
pages = "59--70",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
}