On Gaussian Brunn–Minkowski inequalities

Volume 191 / 2009

Franck Barthe, Nolwen Huet Studia Mathematica 191 (2009), 283-304 MSC: 60E15, 60G15, 52A40, 35K05. DOI: 10.4064/sm191-3-9

Abstract

We are interested in Gaussian versions of the classical Brunn–Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrhard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also yields semigroup proofs of the geometric Brascamp–Lieb inequality and of its reverse form, which follow exactly the same lines.

Authors

  • Franck BartheInstitut de Mathématiques de Toulouse
    Université Paul Sabatier
    31062 Toulouse, France
    e-mail
  • Nolwen HuetInstitut de Mathématiques de Toulouse
    Université Paul Sabatier
    31062 Toulouse, France
    e-mail

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