This is an announcement for the paper "Improved $L_p-$mixed volume inequality for convex bodies" by Van Hoang Nguyen.

Abstract: A sharp quantitative version of the $L_p-$mixed volume inequality is established. This is achieved by exploiting an improved Jensen inequality. This inequality is a generalization of Pinsker-Csisz'ar-Kullback inequality for the Tsallis entropy. Finally, a sharp quantitative version of the $L_p-$Brunn-Minkowski inequality is also proved as a corollary.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 26D15, 52A20, 52A39, 52A40

Remarks: 11 pages, to appear in J. Math. Anal. Appl

Submitted from: vanhoang0610@yahoo.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1506.04250

or

http://arXiv.org/abs/1506.04250