# Kolloquium: M. Henk, TU Berlin: The logarithmic Minkowski problem

The logarithmic Minkowski problem Vortragender: Martin Henk, TU Berlin Einladender: Timm Oertel

Abstract: The classical Minkowski problem asks for necessary and sufficient conditions such that a finite Borel measure on the sphere is the surface area measure of a convex body. In the discrete setting it is the question to decide when a convex polytope with prescribed normal directions and areas of the facets exists. This problem was solved by Minkowski and it is a corner stone of classical Brunn-Minkowski theory. The analogous problem in modern convex geometry and within the L_p-Brunn-Minkowski-theory is known as the L_p-Minkowski problem. Of particular interest is the limit case p=0 and the associated logarithmic Minkowski problem which asks for a characterization of the so called cone volume measure of a convex body. In the discrete setting this leads to the problem to decide when a convex polytope with prescribed normal directions and volumes of the cones generated by the origin and the facets exists. In the talk we survey on the state of the art of the logarithmic Minkowski problem.