The dual Minkowski problem and polytopes

Karoly Boroczky, Central European University and Rényi Institute

April 24, 2018

Around 1900, Minkowski characterized any discrete measure on the unit sphere assigned to a polytope where the measure of a vector in the support is the area of the corresponding facet of the polytope. This theorem initiated the whole field of "Minkowski type problems" on the cross road of PDE, convex geometry and discrete geometry. In this talk, I review some recent results where the path to the solution of Monge-Ampere type differential equations leads to understanding discrete versions for polytopes.