https://neckpinch.com/authors/yu-sun/New arXiv papers by Yu Sun, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2404.05982/arxiv:2404.05982Tue, 09 Apr 2024 00:00:00 GMTGuangming Hu, Ziping Lei, Yu Sun, Puchun Zhou — In this paper, we study the existence and rigidity of (degenerated) circle pattern metric with prescribed total geodesic curvatures in spherical background geometry. To find the (degenerated) circle pattern metric with prescribed total geodesic curvatures, we define some prescribed combinatorial Ricci flows and study the convergence of flows for (degenerated) circle pattern metrics. We solve the prescribed total geodesic curvature problem and provide two methods to find the degenerated circle pattern metric with prescribed total geodesic curvatures. As far as we know, this is the first degenerated result for total geodesic curvatures in spherical background geometry.Ricci flowStability & uniquenessDiscrete & graph Ricci https://neckpinch.com/papers/2311.10528/arxiv:2311.10528Fri, 17 Nov 2023 00:00:00 GMTGuangming Hu, Yi Qi, Yu Sun, Puchun Zhou — This paper investigates a generalized hyperbolic circle packing (including circles, horocycles or hypercycles) with respect to the total geodesic curvatures on the surface with boundary. We mainly focus on the existence and rigidity of circle packing whose contact graph is the 1-skeleton of a finite polygonal cellular decomposition, which is analogous to the construction of Bobenko and Springborn [4]. Motivated by Colin de Verdière's method [6], we introduce the variational principle for generalized hyperbolic circle packings on polygons. By analyzing limit behaviours of generalized circle packings on polygons, we give an existence and rigidity for the generalized hyperbolic circle packing with conical singularities regarding the total geodesic curvature on each vertex of the contact graph. As a consequence, we introduce the combinatoral Ricci flow to find a desired circle packing with a prescribed total geodesic curvature on each vertex of the contact graph.Ricci flowSingularitiesSurfacesStability & uniquenessDiscrete & graph Ricci