Cone volume measure of convex bodies

Gaoyong Zhang, NYU Polytechnic School of Engineering

September 8, 2015

Cone volume measure, like surface area measure, is a fundamental concept of convex bodies in the Euclidean space. It is invariant under special linear transformations, while the surface area measure is not. This makes cone volume measure more essential in affine geometry of convex bodies. The Minkowski existence and uniqueness theorems for surface area measure are classical. For cone volume measure, corresponding theorems are unknown even for convex polygons. This talk explains recent breakthroughs on these problems.