On nonuniqueness of geodesics and geodesic disks in the universal asymptotic Teichmüller space
详细信息 查看全文
- 作者：Yi Qi ; Yan Wu
- 关键词：Asymptotic Teichmüller space ; geodesics ; geodesic disks ; holomorphic isometry ; Teichmüller metric
- 刊名：Acta Mathematica Sinica, English Series
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：33
- 期：2
- 页码：201-209
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- ISSN：1439-7617
- 卷排序：33
文摘
The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmüller space AT(D) are studied in this paper. It is proved that if μ is asymptotically extremal in [[μ]] with hζ*(μ) < h*(μ) for some point ζ ∈ ∂D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [[μ]] in AT(D).