Angle geometry in asymptotic Teichmüller spaces

Yan Wu; Yi Qi

doi:10.1016/j.jmaa.2016.10.014

Angle geometry in asymptotic Teichmüller spaces

Yan Wu^*
, Yi Qi

^*此作品的通讯作者

数学科学学院

Linyi University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

The angular geometry of asymptotic Teichmüller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of AT(X) always exist, it is shown in this paper that there are infinitely many pairs of intersecting geodesic segments such that the angles between them do not exist. The sums of inner angles of geodesic triangles are also studied. It is proved that for any number from 0 to 3π there exists a geodesic triangle in AT(X) such that the sum of its inner angles is equal to such a number.

源语言	英语
页（从-至）	154-166
页数	13
期刊	Journal of Mathematical Analysis and Applications
卷	447
期	1
DOI	https://doi.org/10.1016/j.jmaa.2016.10.014
出版状态	已出版 - 1 3月 2017

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abstract = "The angular geometry of asymptotic Teichm{\"u}ller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of AT(X) always exist, it is shown in this paper that there are infinitely many pairs of intersecting geodesic segments such that the angles between them do not exist. The sums of inner angles of geodesic triangles are also studied. It is proved that for any number from 0 to 3π there exists a geodesic triangle in AT(X) such that the sum of its inner angles is equal to such a number.",

keywords = "Angle, Asymptotic Teichm{\"u}ller space, Geodesic, Teichm{\"u}ller space",

author = "Yan Wu and Yi Qi",

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AU - Qi, Yi

PY - 2017/3/1

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N2 - The angular geometry of asymptotic Teichmüller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of AT(X) always exist, it is shown in this paper that there are infinitely many pairs of intersecting geodesic segments such that the angles between them do not exist. The sums of inner angles of geodesic triangles are also studied. It is proved that for any number from 0 to 3π there exists a geodesic triangle in AT(X) such that the sum of its inner angles is equal to such a number.

AB - The angular geometry of asymptotic Teichmüller spaces is studied. Although it has been proved that the angles between any two geodesic rays from the base point of AT(X) always exist, it is shown in this paper that there are infinitely many pairs of intersecting geodesic segments such that the angles between them do not exist. The sums of inner angles of geodesic triangles are also studied. It is proved that for any number from 0 to 3π there exists a geodesic triangle in AT(X) such that the sum of its inner angles is equal to such a number.

KW - Angle

KW - Asymptotic Teichmüller space

KW - Geodesic

KW - Teichmüller space

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DO - 10.1016/j.jmaa.2016.10.014

M3 - 文章

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SN - 0022-247X

VL - 447

SP - 154

EP - 166

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Angle geometry in asymptotic Teichmüller spaces

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