https://neckpinch.com/authors/yanlin-li/New arXiv papers by Yanlin Li, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2411.06274/arxiv: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 https://neckpinch.com/papers/2404.15705/arxiv:2404.15705Wed, 24 Apr 2024 00:00:00 GMTYanlin Li, Abimbola Abolarinwa, Suraj Ghosh, Shyamal Kumar Hui — In this article we derive gradient estimation for positive solution of the equation \beginequation* (\partial_t-Δ_f)u = A(u)p(x,t) + B(u)q(x,t) + \mathcalG(u) \endequation* on a weighted Riemannian manifold evolving along the (k,m) super Perelman-Ricci flow \beginequation* \frac{\partial g}{\partial t}(x,t)+2Ric_f^m(g)(x,t)\ge -2kg(x,t). \endequation* As an application of gradient estimation we derive a Harnack type inequality along with a Liouville type theorem.Ricci flowHarnack inequalities