| Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces |
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| 作者姓名： | Guang Ming HU Yi QI |
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| 作者单位： | College of Science;LMIB and School of Mathematics and Systems Science |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 11871085, 11371045) |
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| 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.
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| 关 键 词： | TEICHMÜLLER SPACE AUGMENTED TEICHMÜLLER SPACE Strebel ray Busemann points |
Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces |
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| Guang Ming HU,Yi QI.Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces[J].Acta Mathematica Sinica,2020,36(5):605-619. |
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| Authors: | Guang Ming Hu Yi Qi |
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| Institution: | 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 |
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| Abstract: | It is known that every finitely unbranched holomorphic covering π:$$\pi :\tilde{S} \to S$$ of a compact Riemann surface S with genus g ≥ 2 induc |
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| Keywords: | Teichmüller space augmented Teichmüller space Strebel ray Busemann points |
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