Xu Xu, Chao Zheng, Discrete conformal structures on surfaces with boundary (I)---Classification
发布时间：2025-03-12点击次数：
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发表刊物：To appear in Peking Mathematical Journal
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摘要：In this paper, we introduce discrete conformal structures on surfaces with boundary through an axiomatic approach, ensuring that the Poincar´e dual of an ideally triangulated surface with boundary possesses a well-defined geometric structure. We
then classify discrete conformal structures on surfaces with boundary, thereby unifying and generalizing Guo-Luo's generalized circle packings [11], Guo's vertex scalings
[10], and Xu's partial discrete conformal structures [17] on surfaces with boundary. These results extend the work of Glickenstein-Thomas [7] from closed surfaces to surfaces with boundary. Based on the works of Bobenko-Pinkall-Springborn [2] and Zhang-Guo-Zeng-Luo-Yau-Gu [19], we establish the relationships between discrete conformal structures on surfaces with boundary and hyperbolic trigonometry. Surprisingly, we discover that certain subclasses of discrete conformal structures on surfaces with boundary are closely related to the twisted generalized hyperbolic triangles introduced by Roger-Yang [14], a phenomenon absent in the case of closed surfaces [2, 19]. Finally, we investigate the relationships between discrete conformal structures on surfaces with boundary and 3-dimensional hyperbolic geometry by constructing ten types of generalized hyperbolic tetrahedra. Some recently introduced generalized hyperbolic tetrahedra by Belletti-Yang [1] naturally emerge within these constructions.
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论文类型：期刊论文
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是否译文：否
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徐旭
个人信息
博士生导师
硕士生导师- 教师英文名称：Xu Xu
- 教师拼音名称：Xu Xu
- 电子邮箱：
- 学历：研究生毕业
- 办公地点：武汉大学雷军科技楼A430
- 性别：男
- 联系方式：xuxu2@whu.edu.cn
- 毕业院校：中国科学院数学与系统科学研究院
曾获荣誉：
- 国家级青年人才计划
- 湖北省高层次人才特殊支持计划
- 武汉大学弘毅青年学者
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