This is an announcement for the paper "Remarks on the conjectured log-Brunn-Minkowski inequality" by Christos Saroglou.
Abstract: \footnotesize B"{o}r"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality together with its equality cases for pairs of unconditional convex bodies with respect to the same orthonormal basis. Applications of this fact are discussed. Moreover, we prove that the log-Brunn-Minkowski inequality is equivalent to the (B)-Theorem for the uniform measure of the cube (this has been proven by Cordero-Erasquin, Fradelizi and Maurey for the gaussian measure instead).
Archive classification: math.FA
Remarks: Submitted 30 April,2013
Submitted from: saroglou@math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4954
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