Geometry of Riemann surfaces based on closed geodesics

Geometry of Riemann surfaces based on closed geodesics
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基于闭合测地线的黎曼曲面几何

DOI:
10.1090/s0273-0979-98-00750-2
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发表时间:
1998
影响因子:
1.3
通讯作者:
P. S. Schaller
P. S. Schaller
中科院分区:
数学1区
文献类型:
--
作者:
P. S. Schaller

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本文介绍了一个调查的最新结果的几何黎曼曲面显示,研究封闭测地线提供了一个联系不同方面的黎曼曲面理论,如双曲几何,拓扑,谱理论,和理论的算术Fuchsian群。特别感兴趣的是systoles,最短的封闭测地线的表面,他们的研究导致双曲几何的数字密切类似于经典的球包装问题。
The paper presents a survey on recent results on the geometry of Riemann surfaces showing that the study of closed geodesics provides a link between different aspects of Riemann surface theory such as hyperbolic geometry, topology, spectral theory, and the theory of arithmetic Fuchsian groups. Of particular interest are the systoles, the shortest closed geodesics of a surface; their study leads to the hyperbolic geometry of numbers with close analogues to classical sphere packing problems.
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