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On the improvement of concavity of convex measures


Author: Arnaud Marsiglietti
Journal: Proc. Amer. Math. Soc. 144 (2016), 775-786
MSC (2010): Primary 52A20, 52A40; Secondary 28A75, 60G15
DOI: https://doi.org/10.1090/proc/12694
Published electronically: June 24, 2015
MathSciNet review: 3430853
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Abstract: We prove that a general class of measures, which includes $ \log $-concave measures, is $ \frac {1}{n}$-concave according to the terminology of Borell, with additional assumptions on the measures or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch published in 2010.


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Additional Information

Arnaud Marsiglietti
Affiliation: Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France
Email: arnaud.marsiglietti@u-pem.fr

DOI: https://doi.org/10.1090/proc/12694
Keywords: Brunn-Minkowski inequality, convex measure, Gaussian measure
Received by editor(s): April 4, 2014
Received by editor(s) in revised form: December 12, 2014
Published electronically: June 24, 2015
Additional Notes: The author was supported in part by the Agence Nationale de la Recherche, project GeMeCoD (ANR 2011 BS01 007 01).
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society

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