This is an announcement for the paper "Log-concavity properties of Minkowski valuations" by Astrid Berg, Lukas Parapatits, Franz E. Schuster, and Manuel Weberndorfer.

Abstract: New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine previously employed techniques are explored. It is shown that both lead to the same class of Minkowski valuations for which these inequalities hold. An appendix by Semyon Alesker contains the proof of a new classification of generalized translation invariant valuations.

Archive classification: math.MG math.DG math.FA

Mathematics Subject Classification: 52A38, 52B45

Submitted from: franz.schuster@tuwien.ac.at

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

http://front.math.ucdavis.edu/1411.7891

or

http://arXiv.org/abs/1411.7891