数学科学学院学术报告[2024] 015号

(高水平大学建设系列报告895号)

报告题目: Hyperbolic Circle Packings and Total Geodesic Curvatures on Surfaces with Boundary

报告人：胡光明（南京邮电大学）

报告时间：2024年4月9日 9：00-12：00

讲座地点：文科楼1420

报告内容：In this talk we investigate 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. Motivated by Colin de Verdiere's method, we introduce the variational principle for generalized hyperbolic circle packings on polygons. By analyzing limit behaviors of generalized circle packings on polygons, we obtain 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 combinatorial Ricci flow to find a desired circle packing with a prescribed total geodesic curvature on each vertex of the contact graph.

报告人简历：胡光明，博士毕业于北航数学科学学院，现为南京邮电大学理学院讲师。主要研究Teichmuller 空间及模空间的紧化及相关问题，近年来在Ann. Fenn. Math.，Proc. AMS等期刊发表学术论文15篇，主持国家自然科学青年基金一项。

报告邀请人：周泽

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