3-dimensional Combinatorial Yamabe Flow in Hyperbolic Background Geometry
Differential Geometry
2018-05-29 v1 General Relativity and Quantum Cosmology
Geometric Topology
Metric Geometry
Abstract
We study the 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. For a triangulation of a 3-manifold, we prove that if the number of tetrahedra incident to each vertex is at least 23, then there exist real or virtual ball packings with vanishing (extended) combinatorial scalar curvature, i.e. the (extended) solid angle at each vertex is equal to 4{\pi}. In this case, if such a ball packing is real, then the (extended) combinatorial Yamabe flow converges exponentially fast to that ball packing. Moreover, we prove that there is no real or virtual ball packing with vanishing (extended) combinatorial scaler curvature if the number of tetrahedra incident to each vertex is at most 22.
Keywords
Cite
@article{arxiv.1805.10643,
title = {3-dimensional Combinatorial Yamabe Flow in Hyperbolic Background Geometry},
author = {Huabin Ge and Bobo Hua},
journal= {arXiv preprint arXiv:1805.10643},
year = {2018}
}
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34 pages