THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

doi:10.1016/S0252-9602(18)30795-1

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 950-964.doi: 10.1016/S0252-9602(18)30795-1

THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

宋飞, 漆毅, 胡光明

LMIB, School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

收稿日期:2017-05-27 修回日期:2017-09-19 出版日期:2018-06-25 发布日期:2018-06-25
通讯作者: Guangming HU E-mail:18810692738@163.com
作者简介:Fei SONG,E-mail:songfei19860810@163.com;Yi QI,E-mail:yiqi@buaa.edu.cn
基金资助:
This research is supported by the National Natural Science Foundation of China (11371045).

THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

Fei SONG, Yi QI, Guangming HU

LMIB, School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

Received:2017-05-27 Revised:2017-09-19 Online:2018-06-25 Published:2018-06-25
Contact: Guangming HU E-mail:18810692738@163.com
Supported by:
This research is supported by the National Natural Science Foundation of China (11371045).

摘要/Abstract

摘要：

The eventually distance minimizing ray (EDM ray) in moduli spaces of the Riemann surfaces of analytic finite type with 3g +n-3 > 0 is studied, which was introduced by Farb and Masur[5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmüller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given.

关键词: Augmented Teichmüller space, augmented moduli space, Strebel differential, EDM ray

Abstract:

Key words: Augmented Teichmüller space, augmented moduli space, Strebel differential, EDM ray

宋飞, 漆毅, 胡光明. THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES[J]. 数学物理学报(英文版), 2018, 38(3): 950-964.

Fei SONG, Yi QI, Guangming HU. THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES[J]. Acta mathematica scientia,Series B, 2018, 38(3): 950-964.

参考文献

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THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

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