On the improvement of concavity of convex measures

Arnaud Marsiglietti (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Brunn-Minkowski inequality; convex measure; Gaussian measure

Domaines: Analyse fonctionnelle [math.FA]

Arnaud Marsiglietti. On the improvement of concavity of convex measures. 2014. ⟨hal-00967660v2⟩