Monday, November 28, 2016
Technische Universität Berlin
Institut für Mathematik
Str. des 17. Juni 136
10623 Berlin
room MA 041
Lecture - 14:15
Abstract:
Colloquium - 16:00
Abstract:
Joint work with Károly Böröczky Jr. and Martin Henk.
Recently Huang, Lutwak, Yang and Zhang introduced a broad class of geometric measures related to convex bodies. Among these are the dual curvature measures which are the counterparts to the classical curvature measures of convex bodies in the dual Brunn-Minkowski theory. The dual curvature measures generalize the notion of cone-volume measures of polytopes which have been subject to ongoing research and appear in various contexts, e.g. the conjectured log-Brunn-Minkowski inequality. Here we discuss the Minkowski problem associated to dual curvature measures and show necessary conditions on Borel measures on the sphere to be a dual curvature measure of a symmetric polytope. This complements a result of Yiming Zhao who showed, that these conditions are in fact sufficient.