A combinatorial Yamabe problem on two and three dimensional manifolds
Differential Geometry
2016-01-14 v2 Geometric Topology
Abstract
In this paper, we introduce a new combinatorial curvature on two and three dimensional triangulated manifolds, which transforms in the same way as that of the smooth scalar curvature under scaling of the metric and could be used to approximate the Gauss curvature on two dimensional manifolds. Then we use the flow method to study the corresponding constant curvature problem, which is called combinatorial Yamabe problem.
Cite
@article{arxiv.1504.05814,
title = {A combinatorial Yamabe problem on two and three dimensional manifolds},
author = {Huabin Ge and Xu Xu},
journal= {arXiv preprint arXiv:1504.05814},
year = {2016}
}
Comments
We add a proof of the discrete maximal principle in this version