Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces  

作　　者：Guang Ming HU Yi QI 

机构地区：[1]College of Science,Jinling Institute of Technology,Nanjing 211169,P.R.China [2]LMIB and School of Mathematics and Systems Science,Beihang University,Beijing 100191,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第5期605-619,共15页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11871085,11371045)。

摘　　要：It is known that every finitely unbranched holomorphic covering π:S→S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Φπ:Teich(S)→Teich(S).By the mutual relations between Strebel rays in Teich(S)and their embeddings in Teich(S),we show that the 1 st-strata space of the augmented Teichmüller space Teich(S)can be embedded in the augmented Teichmüller space Teich(S)isometrically.Furthermore,we show that Φπ induces an isometric embedding from the set Teich(S)B(∞)consisting of Busemann points in the horofunction boundary of Teich(S)into Teich(S)B(∞)with the detour metric.

关 键 词：TEICHMÜLLER SPACE AUGMENTED TEICHMÜLLER SPACE Strebel ray Busemann points 

分 类 号：O186.12[理学—数学]