On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

Matthieu Fradelizi (1) , Arnaud Marsiglietti (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured the 1/n-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.

Mots clés: entropy power; parallel volume; parallel sets; isoperimetric inequality; Brunn-Minkowski

Domaines: Analyse fonctionnelle [math.FA]

Matthieu Fradelizi, Arnaud Marsiglietti. On the analogue of the concavity of entropy power in the Brunn-Minkowski theory. 2013. ⟨hal-00817113v2⟩