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

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arxiv 1302.6093 v1 pith:S2SOUXGI submitted 2013-02-25 math.FA cs.ITmath.ITmath.MG

Matthieu Fradelizi , Arnaud Marsiglietti This is my paper
classification math.FAcs.ITmath.ITmath.MG
keywords entropyinequalitypowerbrunn-minkowskiconcavityanaloguesimilaritytheory
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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.

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