The Hyperbolic Metric on the Complement of the Integer Lattice Points in the Plane

被引：1
|
作者：
Matsuzaki, Katsuhiko [1 ]
机构：
[1] Waseda Univ, Sch Educ, Dept Math, Tokyo 1698050, Japan
来源：
NEW TRENDS IN ANALYSIS AND INTERDISCIPLINARY APPLICATIONS | 2017年
关键词：
Absolute norm; Continued fraction; Hyperbolic metric; Mathematica; Once-punctured torus; Quasi-isometry; Simple closed geodesic;
D O I：
10.1007/978-3-319-48812-7_31
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A domain in the plane obtained by removing all integer lattice points admits the hyperbolic metric, which is the rank 2 Abelian cover of the once-punctured square tours. We compare the hyperbolic metric of this domain with a scaled Euclidean metric in the complement of the cusp neighborhoods. They are quasi-isometric. We investigate the best possible quasi-isometry constant relying on numerical experiment by Mathematica.
引用
收藏
页码：247 / 252
页数：6
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