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Q_K-Teichmüller空间的Bers嵌入
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作者 唐树安 《数学杂志》 2020年第2期210-218,共9页
本文研究Q_K-Teichmüller空间的Bers投影和预投影.利用拟共形映射理论,证明了Q_KTeichmüller空间的Bers投影和预投影是全纯的.
关键词 拟对称映射 万有Teichmuller空间 QK-Teichmüller空间 Bers投影
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THE REAL HYPER-ELLIPTIC SUBSPACES OF TEICHMüLLER SPACE AND MODULI SPACE
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作者 Guangming HU Yi QI 《Acta Mathematica Scientia》 SCIE CSCD 2019年第4期1121-1135,共15页
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 a... 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 Teichm¨uller 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 Teichm¨uller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article. 展开更多
关键词 TEICHMüller space Strebel RAY moduli space EDM RAY REAL hyper-elliptic subspace
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万有Teichmller空间与Loewner链
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作者 康悦明 《数学年刊(A辑)》 CSCD 北大核心 2010年第6期649-656,共8页
提要通过采用构造Loewner链的方法,得到了单叶函数的充分条件,同时,结合万有Teichm(u|¨)ller空间理论,利用Loewner链构造了单叶函数的拟共形扩张表达式,并且得到了一些拟圆区域的单叶性内径的下界估计不等式.
关键词 单叶函数 万有Teichm(u|¨)ller空间 Loewner链 拟共形扩张 单叶性内径
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THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES
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作者 Fei SONG Yi QI +4 位作者 Guangming HU LMIB School of Mathematics and Systems Science Beihang University 《Acta Mathematica Scientia》 SCIE CSCD 2018年第3期950-964,共15页
The eventually distance minimizing ray(EDM ray) in moduli spaces of the Riemann surfaces of analytic finite type with 3 g + n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance o... The eventually distance minimizing ray(EDM ray) in moduli spaces of the Riemann surfaces of analytic finite type with 3 g + n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmu¨ller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given. 展开更多
关键词 Augmented Teichmüller space augmented moduli space Strebel differential EDM ray
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Local rigidity of the Teichmüller space with the Thurston metric
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作者 Huiping Pan 《Science China Mathematics》 SCIE CSCD 2023年第8期1751-1766,共16页
We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is... We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is an analogue of Royden's theorem concerning the Teichmüller norm. 展开更多
关键词 Teichmüller space Thurston metric Royden's theorem curve complex RIGIDITY
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Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces 被引量:9
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作者 崔贵珍 《Science China Mathematics》 SCIE 2000年第3期267-279,共13页
A quasisymmetric homeomorphism of the unit circle S1 is called integrably asymptotic affine if it admits a quasiconformal extension into the unit disk so that its complex dilatation is square integrable in the Poincar... A quasisymmetric homeomorphism of the unit circle S1 is called integrably asymptotic affine if it admits a quasiconformal extension into the unit disk so that its complex dilatation is square integrable in the Poincaré metric on the unit disk. Let QS* (s1) be the space of such maps. Here we give some characterizations and properties of maps in QS* (S1). We also show that QS* (S1)/M?b (S1) is the completion of Diff(S1)/M?b(S1) in the Weil-Petersson metric. 展开更多
关键词 Teichmüller space Weil-Petersson metric
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Integrable Teichmüller spaces 被引量:2
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作者 郭辉 《Science China Mathematics》 SCIE 2000年第1期47-58,共12页
A new kind of subspaces of the universal Teichmüller space is introduced. Some characterizations of the subspaces are given in terms of univalent functions, Beltrami coefficients and quasisymmetric homeomorphisms... A new kind of subspaces of the universal Teichmüller space is introduced. Some characterizations of the subspaces are given in terms of univalent functions, Beltrami coefficients and quasisymmetric homeomorphisms of the boundary of the unit disc. 展开更多
关键词 the universal teichmüller space SUBspaceS integrable teichmüller spaces
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A function model for the Teichmüller space of a closed hyperbolic Riemann surface 被引量:1
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作者 Yunping Jiang 《Science China Mathematics》 SCIE CSCD 2019年第11期2249-2270,共22页
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... 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. 展开更多
关键词 dual SYMBOLIC space geometric MODEL function MODEL for the TEICHMüller space maximum metric
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On the Geometry of Infinite Dimensional Teichmüller Spaces 被引量:1
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作者 Shen Yuliang (Department of Mathematics,Suzhou University,Suzhou 215006,China) 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1997年第3期413-420,共8页
We prove that in any infinite dimensional Teichmüller space,there exists a minimal geodesic lying in two distinct geodesic disks.
关键词 Quasiconformal mapping Teichmüller space GEODESIC Geodesic disk
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Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces
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作者 Guang Ming HU Yi QI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2020年第5期605-619,共15页
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 ray... 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. 展开更多
关键词 TEICHMüller space AUGMENTED TEICHMüller space Strebel ray Busemann points
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Teichmüller spaces for pointed Fuchsian groups
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作者 SUN MingFeng & SHEN YuLiang Department of Mathematics,Soochow University,Suzhou 215006,China 《Science China Mathematics》 SCIE 2010年第8期2031-2038,共8页
Let T(G) be the Teichmüller space of a Fuchsian group G and T(G) be the pointed Teichmüller space of a corresponding pointed Fuchsian group G.We will discuss the existence of holomorphic sections of the proj... Let T(G) be the Teichmüller space of a Fuchsian group G and T(G) be the pointed Teichmüller space of a corresponding pointed Fuchsian group G.We will discuss the existence of holomorphic sections of the projection from the space M(G) of Beltrami coefficients for G to T(G) and of that from T(G) to T(G) as well.We will also study the biholomorphic isomorphisms between two pointed Teichmüller spaces. 展开更多
关键词 Fuchsian GROUP pointed Fuchsian GROUP TEICHMüller space HOLOMORPHIC SECTION
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A new coordinate of Teichmüller space
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作者 刘劲松 《Science China Mathematics》 SCIE 2001年第12期1523-1530,共8页
By using the theory of quadratic differentials, we give a new coordinate to the Teichmüller space as well as the trajectory structures of a special class of Jenkins-Strebel quadratic differentials.
关键词 Teichmüller space quadratic differentials PANTS
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On the equivalence of extremal Teichmller mapping 被引量:2
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作者 FAN JinHua1 & CHEN JiXiu2 1 Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China 2 School of Mathematical Sciences, Fudan University, Shanghai 200433, China 《Science China Mathematics》 SCIE 2009年第1期77-86,共10页
Let T(△) and B(△) be the Teichmuller space and the infinitesimal Teichmuller space of the unit disk △ respectively. In this paper, we show that [ν]B(△) being an infinitesimal Strebel point does not imply that [ν... Let T(△) and B(△) be the Teichmuller space and the infinitesimal Teichmuller space of the unit disk △ respectively. In this paper, we show that [ν]B(△) being an infinitesimal Strebel point does not imply that [ν]T(△) is a Strebel point, vice versa. As an application of our results, problems proposed by Yao are solved. 展开更多
关键词 Teichmuller space INFINITESIMAL Teichmu¨ller space Strebel POINT
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Hyperbolic Mapping Classes and Their Lifts on the Bers Fiber Space 被引量:2
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作者 Chaohui ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2007年第1期55-66,共12页
Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 + n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the pu... Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 + n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod$ under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mode. 展开更多
关键词 Riemann surfaces Absolutely extremal Teichmüller mapping Mapping classes Teichmiiller spaces Bers fiber spaces
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Koebe Problems and Teichmiiller Theory
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作者 Jin Song LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第3期959-962,共4页
In this paper we study the deformation space of certain Kleinian groups. As a result, we give a new proof of the finite Koebe theorem on Riemann surfaces from a viewpoint of Teichmüller theory.
关键词 Koebe problem Teichmüller space Circle
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A problem in extremal quasiconformal extensions 被引量:2
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作者 漆毅 《Science China Mathematics》 SCIE 1998年第11期1135-1141,共7页
A constantK 0 (m) (h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK 0(h) (indicated by the change in module of the quadrilaterals with vertices o... A constantK 0 (m) (h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK 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 forK 0 (m) (h) =K 1(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK 0 (m) (h)<K 1(h), wherek 1(h) is the maximal dilatation ofh. 展开更多
关键词 quasisymmetric MAPPINGS TEICHMüller spaceS EXTREMAL mapping.
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On the boundary value problem for harmonic maps of the Poincaré disc 被引量:1
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作者 LI ZhongDepartment of Mathematics, Peking University, Beijing 100871, China 《Chinese Science Bulletin》 SCIE EI CAS 1997年第24期2025-2045,共21页
The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmülle... The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfyingwhere ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with normsIt is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B . 展开更多
关键词 Harmonic MAPS quasiconfomial MAPPINGS universal TEICHMüller spaces.
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Remarks on Thurston's Construction of Pseudo-Anosov Maps of Riemann Surfaces 被引量:1
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作者 Chaohui ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2008年第1期85-94,共10页
It is well known that certain isotopy classes of oseudo-Anosov maos on a Riemann surface S of non-excluded type can be defined through Dehn twists tα and tβ along simple closed geodesics α and β on S,respectively.... It is well known that certain isotopy classes of oseudo-Anosov maos on a Riemann surface S of non-excluded type can be defined through Dehn twists tα and tβ along simple closed geodesics α and β on S,respectively. Let G be the corresponding Fuchsian group acting on the hyperbolic plane H so that H/G≌S.For any point α∈S,define S = S/{α}.In this article, the author gives explicit parabolic elements of G from which he constructs pseudo-Anosov classes on S that can be projected to a given pseudo-Anosov class on S obtained from Thurston's construction. 展开更多
关键词 Quasiconformal mappings Riemann surfaces Teichmüller spaces Mapping classes Dehn twists Pseudo-Anosov Bers fiber spaces
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On Strebel points 被引量:1
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作者 HU Yun SHEN YuLiang 《Science China Mathematics》 SCIE 2009年第9期2019-2026,共8页
Any Beltrami coefficient μ on a hyperbolic Riemann surface X of infinite type represents a point [μ]T in the Teichmüller space T (X) and a point [μ]B in the tangent space of T (X) at the base point as well. Th... Any Beltrami coefficient μ on a hyperbolic Riemann surface X of infinite type represents a point [μ]T in the Teichmüller space T (X) and a point [μ]B in the tangent space of T (X) at the base point as well. The paper deals with the problem of determining whether that [μ]T is a Strebel point is equivalent to that [μ]B is an infinitesimal Strebel point. 展开更多
关键词 Teichmüller space Strebel point infinitesimal Strebel point 32G15 30C62 30F60
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Non-Strebel points and variability sets
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作者 漆毅 伍胜健 《Science China Mathematics》 SCIE 2003年第4期525-529,共5页
This paper studies the subset of the non-Strebel points in the universal Teichmüller spaceT. Let z0 ∈ Δ be a fixed point. Then we prove that for every non-Strebel pointh, there is a holomorphic curve γ: [0, 1]... This paper studies the subset of the non-Strebel points in the universal Teichmüller spaceT. Let z0 ∈ Δ be a fixed point. Then we prove that for every non-Strebel pointh, there is a holomorphic curve γ: [0, 1] →T withh as its initial point satisfying the following conditions. (1) The curve γ is on a sphere centered at the base-point ofT, i.e.d T (id, γ(t))=d T (id, h), (t∈[0, 1]). (2) For everyt ∈ (0,1], the variability set Vγ(t)[z0] of γ(t) has non-empty interior, i.e. . 展开更多
关键词 quasiconformal mapping quasisymmetric mapping TEICHMüller space.
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