https://neckpinch.com/authors/bobo-hua/New arXiv papers by Bobo Hua, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.04671arxiv:2609.04671Fri, 04 Sep 2026 00:00:00 GMTShuliang Bai, Bobo Hua — We study the inverse-weight Lin–Lu–Yau Ricci flow on finite trees, and prove the convergence of the curvature on every edge via its diffusion equation. Moreover, the limiting curvature is the unique minimum-norm point of a polyhedron determined by the tree. We characterize possible limits of the normalized edge weights, give criteria for their convergence, and show that different positive initial metrics have equivalent omega-limit sets.Ricci flowDiscrete & graph Ricci https://arxiv.org/abs/2606.09017arxiv:2606.09017Mon, 08 Jun 2026 00:00:00 GMTBobo Hua, Yong Lin, Shuang Liu — In this paper, we consider the Ricci flow with prescribed curvature on infinite graphs, which reads as \beginequation* \fracddtω(t)=-(κ(t)-κ^*)ω(t), t>0, \endequation* where ω is the edge weight, κ and κ^* are Lin-Lu-Yau Ricci curvature and the prescribed curvature on the set of edges, respectively. First, we establish the existence and uniqueness of the solution to the Ricci flow. Furthermore, we prove the convergence of the Ricci flow for graphs with girth at least 6 under two different conditions. Our convergence result aligns with the conclusion of Rodin and Sullivan (J Differ Geom, 26(2) 1987) that a circle packing in the plane with the hexagonal pattern is the regular hexagonal packing.Ricci flowStability & uniquenessDiscrete & graph Ricci https://arxiv.org/abs/2509.22140arxiv:2509.22140Fri, 26 Sep 2025 00:00:00 GMTShuliang Bai, Bobo Hua, Yong Lin, Shuang Liu — In this paper, we study the evolution of metrics on finite trees under continuous-time Ricci flows based on the Lin-Lu-Yau version of Ollivier Ricci curvature. We analyze long-time dynamics of edge weights and curvatures, providing precise characterizations of their limiting behaviors. We prove that the Ricci flow converges to metric with zero curvature on edges whose normalized weights converge to positive values only if the tree is a caterpillar tree.Ricci flowDiscrete & graph Ricci 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/2504.05817arxiv:2504.05817Tue, 08 Apr 2025 00:00:00 GMTHuabin Ge, Bobo Hua, Puchun Zhou — In this paper, we introduce combinatorial Ricci flows (CRFs in short) in Euclidean and hyperbolic background geometries on infinite triangulations of the open disk, which are discrete analogs of Ricci flows on simply connected open surfaces. We establish well-posedness results, the existence and the uniqueness, of CRFs in both Euclidean and hyperbolic background geometries. Moreover, we prove convergence results of CRFs, which indicate a uniformization theorem for CRFs on infinite disk triangulations. As an application, we prove an existence result of circle-packing metrics with infinite prescribed cone angles in hyperbolic background geometry. To our knowledge, these are the first results of CRFs on infinite triangulations.Ricci flowSurfacesStability & uniquenessDiscrete & graph Ricci https://arxiv.org/abs/2402.07475arxiv:2402.07475Mon, 12 Feb 2024 00:00:00 GMTBobo Hua, Yong Lin, Tao Wang — In this paper, we study the Bakry-Émery Ricci flow on finite graphs. Our main result is the local existence and uniqueness of solutions to the Ricci flow. We prove the long-time convergence or finite-time blow up for the Bakry-Émery Ricci flow on finite trees and circles.Ricci flowSingularitiesLimit spaces & RCDStability & uniquenessLong-time existence & convergenceDiscrete & graph Ricci https://arxiv.org/abs/2303.09191arxiv:2303.09191Thu, 16 Mar 2023 00:00:00 GMTHuabin Ge, Bobo Hua, Puchun Zhou — In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under the combinatorial conditions was proved using flow approaches. It remains as an open problem for the spherical case. In this paper, we introduce a combinatorial geodesic curvature flow in spherical background geometry, which is analogous to the combinatorial Ricci flow of Chow and Luo in [4]. We characterize the sufficient and necessary condition for the convergence of the flow. That is, the prescribed geodesic curvature satisfies certain geometric and combinatorial condition if and only if for any initial data the flow converges exponentially fast to a circle pattern with given total geodesic curvature on each circle. Our result could be regarded as a resolution of the problem in the spherical case. As far as we know, this is the first combinatorial curvature flow in spherical background geometry with fine properties, and it provides an algorithm to find the desired ideal circle pattern.Ricci flowOther curvature flowsLong-time existence & convergenceDiscrete & graph Ricci