The Minkowski problem, new constant curvature surfaces in R^3, and some applications

Antonio Alarcon, Rabah Souam

Let $m\in \mathbb{N},$ $m\ge 2,$ and let $\{p_j{\}}_{j=1}^m$ be a finite subset of ${\mathbb{S}}^2$ such that $0\in {\mathbb{R}}^3$ lies in its positive convex hull. In this paper we make…