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

الأصل · EN

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in On the similarity of the entropy power inequality and the Brunn-Minkowski inequality (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) 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.