This is an announcement for the paper "On the analogue of the concavity of entropy power in the Brunn-Minkowski theory" by Matthieu Fradelizi and Arnaud Marsiglietti.
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.
Archive classification: math.FA cs.IT math.IT math.MG
Mathematics Subject Classification: 52A40, 94A17
Submitted from: matthieu.fradelizi@univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.6093
or