On the $L_{p}$-Minkowski problem

Abstract

A volume-normalized formulation of the Lp-Minkowski problem is presented. This formulation has the advantage that a solution is possible for all p ≥ 1, including the degenerate case where the index p is equal to the dimension of the ambient space. A new approach to the Lp-Minkowski problem is presented, which solves the volume-normalized formulation for even data and all p ≥ 1.