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Let X be a non-elementary Riemann surface of type(g,n),where g is the number of genus and n is the number of punctures with 3g-3+n1.Let T(X)be the Teichmller space of X.By constructing a certain subset E of T(X),we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,respectively.This implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics. 相似文献
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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. 相似文献
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《数学物理学报(B辑英文版)》2016,(2)
The geometry of Teichmller metric in an asymptotic Teichmller space is studied in this article. First, a binary infinitesimal form of Teichmller metric on AT(X) is proved.Then, the notion of angles between two geodesic curves in the asymptotic Teichmller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained. 相似文献
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在对数导数意义下,万有Teichmüller空间T1可表示为无穷多个互不相交的连通分支的并集T1={∪θ∈[0,2)Lθ}∪L,研究了该模型分支边界的几何性质,证明了L与Lθ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. 相似文献
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设AT(△)是单位圆盘△上所有渐近Teichmüller等价类[[μ]]或[[f~μ]]构成的渐近Teichmüller空间.本文证明了对AT(△)内的任意渐近极值的f~μ,总存在一个[[f~μ]]内的渐近极值映射g~v,使边界伸缩商h~*(μ_(fog)~(-1)(g(z)))≠0.同时也获得了AT(△)在基点处的切空间上的类似结果. 相似文献
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We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one.Furthermore,we apply this result to the theory of extremal quasiconformal mappings.Let [μ] be a point in the universal Teichmller space such that the Hausdorff dimension of fμ(Δ) is bigger than one.We show that for every kn∈(0,1) and polygonal differentials ψn,n=1,2,...,the sequence {[kn ψn/|ψn|]} cannot converge to [μ] under the Teichmer metric. 相似文献
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Inequalities on the inner radius of univalency and the norm of pre-Schwarzian derivative 总被引:1,自引:0,他引:1
In this paper, we get a lower bound of inner radius of univalency of Schwarzian derivative by means of the norm of pre-Schwarzian derivative. Furthermore, we apply the theory of Universal Teichmuller Space to explain its geometric meaning which shows the relationship between the inner radius in Universal Teichmuller Space embedded by Schwarzian derivative and the norm defined in Universal Teichmuller Space embedded by pre-Schwarzian derivative. 相似文献
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考虑了Strebel点与Hamilton序列之间的关系.这个问题是Gardiner F.P.最早研究的(见[Approximation of infinite-dimensional Tcichmiiller spaces,Trans.Amer.Math.Soc.,1984,282(1):367-383]).在无限小Teichmiiller空间中,证明了范金华在[On infinitesimal Teichmüller space,Bull.Austral Math.Soc.,2008,78:293-300]中得到的使{φ_n}成为Hamilton序列的充分条件不是必要的. 相似文献
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冯小高 《纯粹数学与应用数学》2010,26(5):792-797
在对数导数意义下,万有Teichmuller空间T1可表示为无穷多个互不相交的连通分支的并集.本文研究了该模型各分支的几何性质,给出了为e-iθ/(1-e-iθz)为L和Le的公共边界点,且在‖·‖1的意义下,证明了L,L0,Lθ两两公共边界点之间的距离均为2. 相似文献
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GUO Hui 《中国科学A辑(英文版)》2000,43(1):47-58
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. 相似文献
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In the point view of Lie group, the cross ratio and Schwarzian derivative in Cn are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space Cm
x
n is defined and discussed. It is proved that it is invariant up to similarity under the group of holomorphic automorphism
of the Grassmann manifold CG(m, n). And it is also proved that the Schwarzian derivative equals zero if and only if the mapping is liaearly fractional.
Project supported by the National Natural Science Foundation of China. 相似文献
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Let Γ be a fuchsian group which preserves the unit disc Δ and hence also its complement Δ* in the Riemann sphere
. The Bers embedding represents the Teichm=:uller space T(Γ) of Γ in the space (B (Δ*, Γ) of bounded quadratic differentials for Γ in Δ*. Then, T(Γ) is included in the closed ball centred at the origin of radius 6 inB(Δ*, Γ) with respect to the norm employed in a paper by Nehari [The Schwarzian derivative and Schlicht functions; Bull. Amer.
Math. Soc. 55 (1949), 545–551]. In other words the outradiuso(Γ) ofT(Γ) is not greater than 6. The purpose of this paper is to give a complete characterization of a fuchsian group Γ for which
the outradiuso(Γ) ofT(Γ) attains this extremal value 6. The main theorem is: Let Γ be a fuchsian group preserving Δ*. Then the outradiuso(Γ) of the Teichmüller spaceT(Γ) equals 6 if and only if for any positive numberd, either (i) there exists a hyperbolic disc of radiusd precisely invariant under the trivial subgroup, or (ii) there exists the collar of widthd about the axis of a hyperbolic element of Γ.
Dedicated to Professor K?taro Oikawa on his 60th birthday 相似文献
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设ψ : D → Ω 是一个单叶函数, 利用Schwarzian 导数, 本文获得了log ψ′ 属于QK 空间的一个充要条件. 此外, 本文运用了一个几何条件来刻画QK 空间. 相似文献