https://neckpinch.com/authors/yong-lin/New arXiv papers by Yong Lin, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT 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/2603.10479arxiv:2603.10479Wed, 11 Mar 2026 00:00:00 GMTYong Lin, Shuang Liu — In this paper, we consider the Ricci flow with prescribed curvature on the finite graph G=(V,E). For any e in E, (dω(t,e))/dt = −(κ(t,e)−κ^*(e))ω(t,e), t > 0, where ω is the weight function, κ is Lin-Lu-Yau Ricci curvature, and κ^* is the prescribed curvature. By imposing invariance of the graph distance with respect to time t, the Ricci flow introduced above characterizes the weight evolution governed by the Lin-Lu-Yau curvature. We first establish the existence and uniqueness of the solution to this equation on general graphs. Furthermore, for graphs with girth of at least 6, we prove that the Ricci flow converges exponentially to weights of κ^* if and only if κ^* is attainable (namely, there exist weights realizing κ^*). In particular, we prove that the weights for constant curvature exist if and only if max_(∅ ≠ Ωsubsetneq V) (|E(Ω)|)/(|Ω|) < (|E|)/(|V|), where E(Ω) denotes the set of edges within the induced subgraph of Ω, and |A| is the cardinality of the set A. Viewing edge weights as metrics on surface tilings with girth of at least 5 or the duals of triangulations with vertex degrees exceeding 5, we demonstrate that our constant Lin-Lu-Yau curvature flow serves as an analog to the 2D combinatorial Ricci flow for piecewise constant curvature metrics, thereby providing an affirmative answer to Question 2 posed by Chow and Luo (J Differ Geom, 63(1) 2002).Ricci flowOther curvature flowsSurfacesStability & uniquenessLong-time existence & convergenceDiscrete & 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/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