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1.
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.  相似文献   

2.
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.  相似文献   

3.
Let T(S) be a Teichmüller space of a hyperbolic Riemann surface S, viewed as a set of Teichmüller equivalence classes of Beltrami differentials on S. It is shown in this paper that for any extremal Beltrami differential μ0 at a given point τ of T(S), there is a Hamilton sequence for μ0 formed by Strebel differentials in a natural way. Especially, such a kind of Hamilton sequence possesses some special properties. As applications, some results on point shift differentials are given.  相似文献   

4.
LetT be the universal Teichmüller space viewed as the set of all normalized quasisymmetric homeomorphism of the unit circleS 1=∂Δ. Denote byV h [z 0] the variability set ofz 0 with respect toh∈T. The following is proved: Leth 0 be a point ofT. Suppose thatμ 0 is an arbitrarily given extremal Beltrami differential ofh 0 andf 0: μ→μ is a quasiconformal mapping with the Beltrami coefficientμ 0 andf 01s=h 0. Then there are a sequenceh n of points inT and a sequencew n of points in Δ withh n ∈(Δ−V h [z 0]) andw n f 0(z 0) andh n h 0 andn∞ such that the point shift differentials determined byh n asw n form a Hamilton sequence ofμ 0. Project supported by the National Natural Science Foundation of China (Grant No. 19531060) and the Doctoral Education Program Foundation of China.  相似文献   

5.
Na SUN 《数学学报(英文版)》2007,23(10):1909-1914
In this paper, we introduce an operator Hμ(z) on L^∞(△) and obtain some of its properties. Some applications of this operator to the extremal problem of quasiconformal mappings are given. In particular, a sufficient condition for a point r in the universal Teichmfiller space T(△) to be a Strebel point is obtained.  相似文献   

6.
LetT(S) be the Teichmüller space of a Riemann surfaceS. By definition, a geodesic disc inT(S) is the image of an isometric embedding of the Poincaré disc intoT(S). It is shown in this paper that for any non-Strebel pointτ ∈ T(S), there are infinitely many geodesic discs containing [0] and τ.  相似文献   

7.
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 and determining the biholomorphic isomorphisms of these fiber spaces.  相似文献   

8.
The aim of this paper is to develop the theory of a compactification of Teichmüller space given by F. Gardiner and H. Masur, which we call the Gardiner–Masur compactification of the Teichmüller space. We first develop the general theory of the Gardiner–Masur compactification. Secondly, we will investigate the asymptotic behaviors of Teichmüller geodesic rays under the Gardiner–Masur embedding. In particular, we will observe that the projective class of a rational measured foliation G can not be an accumulation point of every Teichmüller geodesic ray under the Gardiner–Masur embedding, when the support of G consists of at least two simple closed curves. Dedicated to Professor Yoichi Imayoshi on the occasion of his 60th birthday.  相似文献   

9.
It is proved that, for any elementary torsion free Fuchsian group F, the natural projection from the Teichmiiller curve V(F) to the Teichmiiller space T(F) has no holomorphic section.  相似文献   

10.
We formulate and describe a visual compactification of the Teichmüller space by Weil–Petersson geodesic rays emanating from a point X. We focus on analogies with Bers’s compactification: due to noncompleteness, finite rays correspond to cusps, and such cusps are dense in the visual sphere. By analogy with a result of Kerckhoff and Thurston, we show the natural action of the mapping class group does not extend continuously to the visual compactification. We conclude with examples that distinguish the visual boundary from Bers’s boundary for Teichmüller space Research partially supported by NSF Grants DMS 0204454 and 0354288  相似文献   

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