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

页码：247 / 252

页数：6

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