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
After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal...After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal Teichmüller space.In particular,we show that the Faber operator acts as a bounded operator on BMOA if the symbol conformal map stays nearly to the base point in the BMO-Teichmüller space.Meanwhile,we obtain several results on quasiconformal mappings,BMOTeichm¨uller space and chord-arc curves as well.As by-products,this provides a complex analysis approach to the boundedness of the Cauchy integral acting on BMO functions on a chord-arc curve near to the unit circle in the BMO-Teichmüller space.展开更多
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
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
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
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.
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
We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between 'punctured' Teichmuller c...We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between 'punctured' Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.展开更多
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
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
根据[fv]=12-vzz2∈L,给出了魏寒柏"关于万有Teichmüller空间T1的分支"一文中定理2.1的简洁证明;构造了具体的解析函数fλ(z),使其当λ>0时:fλ∈L0,当λ<0时:fλ∈Lθ,从而简化了王哲"The Distance be-tween...根据[fv]=12-vzz2∈L,给出了魏寒柏"关于万有Teichmüller空间T1的分支"一文中定理2.1的简洁证明;构造了具体的解析函数fλ(z),使其当λ>0时:fλ∈L0,当λ<0时:fλ∈Lθ,从而简化了王哲"The Distance be-tween Different Component of the Universal Teichmüller Space"一文中定理2.2的证明.展开更多
文摘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.
文摘After reviewing Grunsky operator and Faber operator acting on Dirichlet space,we discuss the boundedness of Faber operator on BMOA,a new subject which turns out to be closely related to the BMO theory of the universal Teichmüller space.In particular,we show that the Faber operator acts as a bounded operator on BMOA if the symbol conformal map stays nearly to the base point in the BMO-Teichmüller space.Meanwhile,we obtain several results on quasiconformal mappings,BMOTeichm¨uller space and chord-arc curves as well.As by-products,this provides a complex analysis approach to the boundedness of the Cauchy integral acting on BMO functions on a chord-arc curve near to the unit circle in the BMO-Teichmüller space.
基金supported by National Natural Science Foundation of China (Grant No.11901241).
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by the National Science Foundation of USA (Grant No. DMS1747905)collaboration grant from the Simons Foundation (Grant No. 523341)+1 种基金the Professional Staff Congress of the City University of New York Award (Grant No. PSC-CUNY 66806-00 44)National Natural Science Foundation of China (Grant No. 11571122)
文摘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.
基金The authors would like to thank the referee for his many valuable suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 10231040).
文摘We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between 'punctured' Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.
基金supported by the Program for New Century Excellent Talents in University(Grant No.06-0504)National Natural Science Foundation of China (Grant No.10771153)
文摘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.
基金Supported by National Natural Science Foundation of China(Grant Nos.11871085,11371045)。
文摘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.
文摘根据[fv]=12-vzz2∈L,给出了魏寒柏"关于万有Teichmüller空间T1的分支"一文中定理2.1的简洁证明;构造了具体的解析函数fλ(z),使其当λ>0时:fλ∈L0,当λ<0时:fλ∈Lθ,从而简化了王哲"The Distance be-tween Different Component of the Universal Teichmüller Space"一文中定理2.2的证明.
基金Supported by National Natural Science Foundation of China(11601100)the Joint Foundation of Guizhou Provincial Science and Technology Department([2017]7337,[2017]5726).
