Analysis Seminar

The Logarithmic Minkowski Problem

Speaker: Gaoyong Zhang, NYU Polytechnic School of Engineering

Location: Warren Weaver Hall 1302

Date: Thursday, February 12, 2015, 11 a.m.


The logarithmic Minkowski problem, like the classical Minkowski problem, is a fundamental question in the affine geometry of convex bodies. For symmetric convex bodies, it asks what are the necessary and sufficient conditions for a measure in (n-1)-dimensional projective space to be the cone-volume measure of the unit ball in an n-dimensional normed space. Solving this problem is equivalent to establishing existenceof a solution to a Monge-Ampere equation. This talk outlines a complete solution to the symmetric logarithmic Minkowski problem and will present related open problems.