https://neckpinch.com/authors/shengyu-li/New arXiv papers by Shengyu Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2504.11266arxiv:2504.11266Tue, 15 Apr 2025 00:00:00 GMTShengyu Li, Zhi-Gang Wang — The aim of this paper is to investigate the fractional combinatorial Calabi flow for hyperbolic bordered surfaces. By Lyapunov theory, it is proved that the flow exists for all time and converges exponentially to a conformal factor that generates a hyperbolic surface whose lengths of boundary components are prescribed positive numbers. Furthermore, a generalized combinatorial Yamabe flow is introduced in the same geometry setting, with the long time existence and convergence established. This result yields an algorithm for searching bordered surfaces, which may accelerate convergence speed.Yamabe flowOther curvature flowsKähler geometryLong-time existence & convergence https://arxiv.org/abs/2501.01678arxiv:2501.01678Fri, 03 Jan 2025 00:00:00 GMTShengyu Li, Zhigang Wang — We study the combinatorial Calabi flow for ideal circle patterns in both hyperbolic and Euclidean background geometry. We prove that the flow exists for all time and converges exponentially fast to an ideal circle pattern metric on surfaces with prescribed attainable curvatures. As a consequence, we provide an algorithm to find the desired ideal circle patterns.Other curvature flowsSurfacesKähler geometryLong-time existence & convergence https://arxiv.org/abs/2204.08191arxiv:2204.08191Mon, 18 Apr 2022 00:00:00 GMTShengyu Li, Xu Xu, Ze Zhou — This paper studies the combinatorial Yamabe flow on hyperbolic bordered surfaces. We show that the flow exists for all time and converges exponentially fast to conformal factor which produces a hyperbolic surface whose lengths of boundary components are equal to prescribed positive numbers. This provides an algorithm to such problems.Yamabe flowLong-time existence & convergence