A Discrete Uniformization Theorem for Polyhedral Surfaces

Abstract

We introduce a discrete conformality for polyhedral metrics on surfaces. It is shown that each polyhedral metric on a surface is discretely conformal to a constant curvature polyhedral metric which is unique up to scaling. Furthermore, the constant curvature metric can be found by a finite dimensional variational principle. This is joint work with David Gu, Jian Sun and Tianqi Wu.