On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space  

作　　者：Yi QI Yan WU 

机构地区：[1]LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, P. R. China [2]School of Science, Linyi University, Linyi 276005, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2017年第2期201-209,共9页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11371045)

摘　　要：Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （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）.Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （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）.

关 键 词：Asymptotic Teichmuller space GEODESICS geodesic disks holomorphic isometry Teichmul-ler metric 

分 类 号：O177[理学—数学]