关于Teichmüller极值的等价性

分别记T(Δ)与B(Δ)为单位圆盘Δ上的Teichmüller空间与无限小Teichmüller空间.证明了|v|B(Δ)是无限小Strebel点并不能说明|v|T(Δ)是一个Strebel点以及|v|T(Δ)是Strebel点并不能说明|v|B(Δ)是一个无限小Strebel点.作为这个结论的应用,解决了姚国武提出的问题.     

Teichmüller空间上纤维空间之间的同构

主要研究Teichmüller空间上一些重要的纤维空间,包括Bers纤维空间和Teichmüller曲线．证明“穿孔”Teichmüller曲线之间的一个同构定理,并研究这些纤维空间之间的双全纯同构．     

On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmüller space AT(D) are studied in this paper. It is proved that if μ is asymptotically extremal in [[μ]] with h_ζ~*(μ) h~*(μ) for some point ζ∈ ?D, then there exist infinitely many geodesic segments joining [[0]]and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [[μ]] in AT(D).     

Strebel点

无限型Riemann曲面X上的一个Beltrami系数μ确定了Teichmüller空间T（X）中的一个点[μ]T,同时也确定了T（X）在基点处的切空间中的一个点[μ]B.本文讨论[μ]T是一个Strebel点和[μ]B是一个无穷小Strebel点的等价性问题.     

Bloch函数到BMOA空间的距离

本文利用高阶导数形式给出了Bloch函数到BMOA空间的距离刻画.这些结论推广了由Peter Jones和赵如汉等人所得到的一阶导数形式的距离公式.作为应用,我们给出了关于小Teichmüller空间的一些等价刻画.     

万有Teichmüller空间对数导数嵌入模型的一些性质

在对数导数意义下,万有Teichmüller空间T_1可表示为无穷多个互不相交的连通分支的并集T_1={■ L_θ}∪L,研究了该模型分支边界的几何性质,证明了L与L_θ的边界存在无穷多个公共点,同时还解决了关于一个分支中的点到另一分支中心距离上确界的公开问题．     

万有Teichmüller空间与Loewner链

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Teichmüller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.     

双曲区域上的Teichmüller极值映射

本文讨论双曲区域上的极值映射，构造了两个Ｔｅｉｃｈｍüｌｅｒ极值映射，并对由圆锥曲线界成的区域的极值情况作了分类．     

Stable Teichmller mappings of type (0,4)

Let X = C\{0,1} and X = X\{}. We get a necessary and suficient condition on the position of  in X such that X has stable Teichmller mappings. Furthermore, we can formulate all these stable Teichmller mappings. The main result in this paper partially answers a question posed by Kra.     

Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms

Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.     

Endpoint estimates of generalized homogeneous Littlewood–Paley <Emphasis Type="Italic">g</Emphasis>-functions over non-homogeneous metric measure spaces

Let (χ, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Under the weak reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function_r (r∈[2,∞)) is bounded from Hardy space H¹(μ) into L¹(μ). Moreover, the authors show that, if f ∈ RBMO(μ), then[_r(f)]^r is either infinite everywhere or finite almost everywhere, and in the latter case,[_r(f)]^r belongs to RBLO(μ) with the norm no more than ‖f‖_RBMO(μ) multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of_r from RBMO(μ) into RBLO(μ). The vector valued Calderón-Zygmund theory over (χ, d, μ) is also established with details in this paper.     

Local boundary dilatation attained by asymptotical extremal

In this paper, we prove that the local boundary dilatation at a boundary point can be attained by an asymptotically extremal representative in a Teichmüller equivalence class.     

Some remarks on the geodesics in infinite dimensional Teichmüller spaces

LetB denote the set of those pointsp in an infinite dimensional Teichmüller space such that a geodesic between the zero point andp is not unique. Some properties of the setB are given.     

Strebel differentials and Hamilton sequences

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.     

非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈[0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.     

On geodesics in asymptotic Teichm��ller spaces

Let R be a Riemann surface of infinite analytic type, T(R) and AT(R) be the Teichmüller space and asymptotic Teichmüller space on R respectively. The purpose of this paper is to discuss some problems related to geodesics in AT(R). It is proved that uniqueness of geodesics joining two given points [??] and [??] in T (R) dose not imply uniqueness of geodesics joining?[[??]] and [[??]] in AT(R). Furthermore, a Beltrami differential??? is constructed such that there are infinitely many geodesics joining [[0]] and?[[??]] in AT(R), and a sufficient condition to determine the difference of the geodesics [[t?? ₁]] and [[t?? ₂]] (0??? t??? 1) joining [[0]] and?[[??]] in AT(??) is given.     

A quasiconformal mapping class group acting trivially on the asymptotic Teichmüller space

For an analytically infinite Riemann surface , the quasiconformal mapping class group always acts faithfully on the ordinary Teichmüller space . However in this paper, an example of is constructed for which acts trivially on its asymptotic Teichmüller space .

     

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

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.