Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry
Differential Geometry
2024-07-12 v1 Geometric Topology
Abstract
This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realized by a degenerated circle packing or not. We fully characterize the sufficient and necessary conditions and show the uniqueness. Furthermore, we introduce the combinatoral Ricci flow to find the desired degenerated circle packed surface, analougus to the methods of Chow-Luo and Takatsu.
Keywords
Cite
@article{arxiv.2407.08496,
title = {Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry},
author = {Guangming Hu and Sicheng Lu and Dong Tan and Youliang Zhong and Puchun Zhou},
journal= {arXiv preprint arXiv:2407.08496},
year = {2024}
}
Comments
36 pages, 9 figures