https://neckpinch.com/authors/yi-qi/New arXiv papers by Yi Qi, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2403.05777/arxiv:2403.05777Sat, 09 Mar 2024 00:00:00 GMTGuangming Hu, Ziping Lei, Yi Qi, Puchun Zhou — In hyperbolic background geometry, we investigate a generalized circle packing (including circles, horocycles and hypercycles) with conical singularities on a surface with boundary, which has a total geodesic curvature on each generalized circle of this circle packing and a discrete Gaussian curvature on the center of each dual circle. The purpose of this paper is to find this type of circle packings with prescribed total geodesic curvatures on generalized circles and discrete Gaussian curvatures on centers of dual circles. To achieve this goal, we firstly establish existence and rigidity on this type of circle packings by the variational principle. Secondly, for p>1, we introduce combinatorial p-th Calabi flows to find the circle packing with prescribed total geodesic curvatures on generalized circles and discrete Gaussian curvatures on centers of dual circles for the first time.Other curvature flowsSingularitiesSurfacesKähler geometryStability & uniquenessKähler–Einstein & K-stabilityDiscrete & 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