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

Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces
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紧双曲黎曼曲面Teichmüller空间边界子集的等距嵌入

DOI:
10.1007/s10114-020-8096-z
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发表时间:
2020
期刊:
Acta Mathematica Sinica, English Series
影响因子:
--
通讯作者:
Y. Qi
Y. Qi
中科院分区:
--
文献类型:
--
作者:
Guangming Hu;Y. Qi

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It is known that every finitely unbranched holomorphic coveringπ:of a compact Riemann surfaceSwith genusg≥ 2 induces an isometric embedding. By the mutual relations between Strebel rays inTeich(S) and their embeddings in, we show that the 1st-strata space of the augmented Teichmüller spacecan be embedded in the augmented Teichmüller spaceisometrically. Furthermore, we show that Φπinduces an isometric embedding from the setTeich(S)B(∞) consisting of Busemann points in the horofunction boundary ofTeich(S) intowith the detour metric.
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