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

Published 25 Feb 2013 in math.FA, cs.IT, math.IT, and math.MG | (1302.6093v1)

Abstract: Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in {\it On the similarity of the entropy power inequality and the Brunn-Minkowski inequality} (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the $\frac{1}{n}$-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.