https://neckpinch.com/authors/hao-yu/New arXiv papers by Hao Yu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2506.07130arxiv:2506.07130Sun, 08 Jun 2025 00:00:00 GMTXiaorui Yang, Hao Yu — This paper presents a comprehensive study of the combinatorial p-th Calabi flow for both finite and infinite ideal circle patterns. In the finite case, we establish a sharp criterion: the combinatorial p-th Calabi flow with p>1 converges if and only if a constant curvature metric exists in the underlying geometric background. In the infinite setting, we prove the long-time existence of solutions to the combinatorial p-th Calabi flow for p ≥ 2, representing a significant advance in the theory of curvature flows on infinite structures.Other curvature flowsKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability https://arxiv.org/abs/2506.05036arxiv:2506.05036Thu, 05 Jun 2025 00:00:00 GMTHuabin Ge, Bobo Hua, Hao Yu, Puchun Zhou — In his seminal work, Rivin characterized finite ideal polyhedra in three-dimensional hyperbolic space. However, the characterization of infinite ideal polyhedra, as proposed by Rivin, has remained a long-standing open problem. In this paper, we introduce the combinatorial Ricci flow for infinite ideal circle patterns, a discrete analogue of Ricci flow on non-compact Riemannian manifolds, and prove a characterization of such circle patterns under certain combinatorial conditions. Our results provide affirmative solutions to Rivin's problem.Ricci flow3-manifoldsBoundaries & non-compactDiscrete & graph Ricci https://arxiv.org/abs/2505.05925arxiv:2505.05925Fri, 09 May 2025 00:00:00 GMTChang Li, Yangxiang Lu, Hao Yu — Since the fundamental work of Chow-Luo, Ge et al., the combinatorial curvature flow methods became a basic technique in the study of circle pattern theory. In this paper, we investigate the combinatorial Ricci flow with prescribed total geodesic curvatures in spherical background geometry. For infinite cellular decompositions, we establish the existence of a solution to the flow equation for all time. Furthermore, under an additional condition, we prove that the solution converges as time tends to infinity. To the best of our knowledge, this is the first study of an infinite combinatorial curvature flow in spherical background geometry.Ricci flowOther curvature flowsDiscrete & graph Ricci https://arxiv.org/abs/2411.06274arxiv:2411.06274Sat, 09 Nov 2024 00:00:00 GMTGuangming Hu, Ziping Lei, Yanlin Li, Hao Yu — In 1991, Beardon and Stephenson [2] generalized the classical Schwarz-Pick lemma in hyperbolic geometry to the discrete Schwarz-Pick lemma for Andreev circle packings. This paper continues to investigate the discrete Schwarz-Pick lemma for generalized circle packings (including circle, horocycle or hypercycle) in hyperbolic background geometry. Since the discrete Schwarz-Pick lemma is to compare some geometric quantities of two generalized circle packings with different boundary values, we first show the existence and rigidity of generalized circle packings with boundary values, and then we introduce the method of combinatorial Calabi flows to find the generalized circle packings with boundary values. Moreover, motivated by the method of He [21], we propose the maximum principle for generalized circle packings. Finally, we use the maximum principle to prove the discrete Schwarz-Pick lemma for generalized circle packings.Other curvature flowsKähler geometryStability & uniquenessDiscrete & graph Ricci