Sicheng Lu — Neckpinchhttps://neckpinch.com/authors/sicheng-lu/New arXiv papers by Sicheng Lu, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometryhttps://neckpinch.com/papers/2407.08496/arxiv:2407.08496Thu, 11 Jul 2024 00:00:00 GMTGuangming Hu, Sicheng Lu, Dong Tan, Youliang Zhong, Puchun Zhou — 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.Ricci flowStability & uniquenessDiscrete & graph Ricci