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

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Acta Mathematica Sinica,English Series 2020年第5期36卷 605-619页

作者： Guang Ming HU Yi QI College of Science Jinling Institute of TechnologyNanjing 211169P.R.China LMIB and School of Mathematics and Systems Science Beihang UniversityBeijing 100191P.R.China

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

THE REAL HYPER-ELLIPTIC SUBSPACES OF teichmüller SPACE AND MODULI SPACE

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Acta Mathematica Scientia 2019年第4期39卷 1121-1135页

作者：胡光明漆毅 LMIB School of Mathematics and Systems Science Beihang University

Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in teichmüller spaces and moduli spaces, respectively. Motivated by the study of [3, 9], two special kinds of Strebel rays in the real hyper-elliptic subspace of teichmüller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.

关键词： teichmüller space Strebel ray moduli space EDM ray real hyper-elliptic subspace

A function model for the teichmüller space of a closed hyperbolic Riemann surface

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Science China Mathematics 2019年第11期62卷 2249-2270页

作者： Yunping Jiang Department of Mathematics Queens College of the City University of New York Department of Mathematics The CUNY Graduate Center

We introduce a function model for the teichmüller space of a closed hyperbolic Riemann surface.Then we introduce a new metric on the teichmüller space by using the maximum norm on the function space.We prove that the identity map from the teichmüller space equipped with the teichmüller metric to the teichmüller space equipped with this new metric is uniformly continuous. Moreover, we prove that the inverse of the identity, i.e., the identity map from the teichmüller space equipped with this new metric to the teichmüller space equipped with the teichmüller metric, is continuous(but not uniformly). Therefore, the topology induced by the new metric is the same as the topology induced by the teichmüller metric on the teichmüller space.Finally, we give a remark about the pressure metric on the function model and the Weil-Petersson metric on the teichmüller space.

关键词： dual symbolic space geometric model function model for the teichmüller space maximum metric

Geodesic discs in teichmüller space

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Science China Mathematics 2005年第8期48卷 1075-1082页

作者： LI Zhong LMAM & School of Mathematical Sciences Peking University Beijing 100871 China

Let T(S) be the teichmüller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincaré disc into T(S). It is shown in this paper that for any non-Stre... 详细信息

关键词： teichmüller space, geodesic discs.

Isomorphisms of fiber spaces over teichmüller spaces

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Science China Mathematics 2006年第7期49卷 877-892页

作者： HU Yun SHEN Yuliang Department of Mathematics Suzhou University Suzhou 215006 China Department of Mathematics Suzhou University Suzhou 215006 China

We will be mainly concerned with some important fiber spaces over teichmüller spaces, including the Bers fiber space and teichmüller curve, establishing an isomorphism theorem between "punctured" teichmüller curves... 详细信息

关键词： teichmüller space, Bers fiber space, "punctured" fiber space, teichmüller curve, "punctured" teichmüller curve, biholomorphic isomorphism.

An isomorphism theorem for teichmüller curves

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Science China Mathematics 2006年第5期49卷 577-586页

作者： CAI Yongmao SHEN Yuliang Department of Mathematics Suzhou University Suzhou 215006China Department of Mathematics Suzhou University Suzhou 215006China

It is proved that for any Fuchsian group Γ such that H/Γ is a hyperbolic Riemann surface, the teichmüller curve V(Γ) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Γ) onto V(Γ) is holomorphic with local holomorphic sections.An isomorphism theorem for teichmüller curves is deduced, which generalizes a classical result that the teichmüller curve V(Γ) depends only on the type of Γ and not on the orders of the elliptic elements of Γ when H/Γ is a compact hyperbolic Riemann surface.

关键词： teichmüller space, Bers fiber space, teichmüller curve, biholomorphic isomorphism.

A problem in extremal quasiconformal extensions

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Science China Mathematics 1998年第11期41卷 1135-1141页

作者：漆毅 School of Mathematical Sciences Peking University Beijing China

A constant K (m) 0(h) is introduced for every quasisymmetric mapping h of the unit circle and every integer m ≥4 which contains the constant K 0(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and sufficient condition is established for K (m) 0(h)=K 1(h) . It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property that K (m) 0(h)

关键词： quasisymmetric mappings teichmüller spaces extremal mapping.

Local boundary dilatation of quasiconformal maps

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Science China Mathematics 2005年第6期48卷 798-807页

作者： QI Yi Department of Applied Mathematics LIMB of the Ministry of Education Beijing University of Aeronautics and Astronautics Beijing 100083 China

By studying the existence problem of locally extremal Beltrami differential posed by F. Gardiner and N. Lakic, we introduce a new definition of the local boundary the same as the usual ones in the case of Jordan domains. Then we show that the answer to the problem of F. Gardiner and N. Lakic is affirmative according to this new definition. Comparing with the usual definitions, the problem of F. Gardiner and N. Lakic is partly answered and the results of G. Cui and Y. Qi is generalized.

关键词： quasiconformal map, teichmüller space.

拟共形映照的极值问题与teichmüller理论

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数学进展 1985年第1期 23-38页

作者：李忠北京大学

本文的目的是综合介绍Riemann曲面上的拟共形映照极值问题的研究,以及与这种研究有关的 teichmuller理论。 §1 teichmuller 极值问题（1）早在拟共形映照这个词正式见于文献之前,H.Grozsch 就提出并解决了一类非共形映照的极值问题... 详细信息

本文的目的是综合介绍Riemann曲面上的拟共形映照极值问题的研究,以及与这种研究有关的 teichmuller理论。 §1 teichmuller 极值问题（1）早在拟共形映照这个词正式见于文献之前,H.Grozsch 就提出并解决了一类非共形映照的极值问题（参看[22]）.设f:x+iy→u+iv是矩形R:0≤x≤a,0≤y≤1到矩形R1:0≤u≤b,0≤v≤1的连续可微映照,把矩形R映照为矩形R1,且保持顶点对应:0→0,a→

关键词：共形映照 teichmüller 极值问题 Riemann 连续可微全纯二次微分边界对应伸缩商单位圆