共查询到20条相似文献,搜索用时 93 毫秒
1.
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. 相似文献
2.
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
3.
Huiping Pan 《中国科学 数学(英文版)》2023,(8):1751-1766
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. 相似文献
4.
《中国科学 数学(英文版)》2016,(10)
We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compactification of Teichm¨uller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into the space of geodesic currents, we prove that a horocycle path in Teichm¨uller space, which is induced by a quadratic differential whose vertical measured foliation is uniquely ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary. 相似文献
5.
Masahiro YANAGISHITA 《数学学报(英文版)》2014,(4)
Being a Strebel point gives a sufficient condition for that the extremal Beltrami coefficient is uniquely determined in a Teichmüller equivalence class.We consider how Strebel points are characterized.In this paper,we will give a new characterization of Strebel points in a certain subset of the universal Teichmüller space by a property of the Grunsky operator. 相似文献
6.
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. 相似文献
7.
Grunsky operators play an important role in classical geometric function theory and in the study of Teichmüller spaces. The Grunsky map is known to be holomorphic on the universal Teichmüller space. In this paper the authors deal with the compactness of a Grunsky differential operator. They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator. 相似文献
8.
TANG ShuAn 《中国科学 数学(英文版)》2013,56(3):541-551
In this paper, we prove that the Bers projection of the integrable Teichmller space is holomorphic. By using the Douady-Earle extension, we obtain some characterizations of the integrable Teichmller space as well as the p-integrable asymptotic affine homeomorphism. 相似文献
9.
《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
10.
Masahiro Yanagishita 《分析论及其应用》2014,(1)
The Strebel point is a Teichm ¨uller equivalence class in the Teichm ¨uller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper,we give a sufficient condition in terms of the Schwarzian derivative for a Teichm ¨uller equivalence class of the universal Teichm ¨uller space under which the class is a Strebel point. As an application, we construct a Teichm ¨uller equivalence class that is a Strebel point and that is not an asymptotically conformal class. 相似文献
11.
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
12.
On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space
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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). 相似文献
13.
14.
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
15.
To any compact hyperbolic Riemann surface X, we associate a new type of automorphism group — called its commensurability automorphism group, ComAut(X). The members of ComAut(X) arise from closed circuits, starting and ending at X, where the edges represent holomorphic covering maps amongst compact connected Riemann surfaces (and the vertices represent
the covering surfaces). This group turns out to be the isotropy subgroup, at the point represented by X (in $ T_\infty $), for the action of the universal commensurability modular group on the universal direct limit of Teichmüller
spaces, $ T_\infty $. Now, each point of $ T_\infty $ represents a complex structure on the universal hyperbolic solenoid.
We notice that ComAut(X) acts by holomorphic automorphisms on that complex solenoid. Interestingly, this action turns out to be ergodic (with respect
to the natural measure on the solenoid) if and only if the Fuchsian group uniformizing X is arithmetic. Furthermore, the action of the commensurability modular group, and of its isotropy subgroups, on some natural vector bundles
over $ T_\infty $, are studied by us. 相似文献
16.
E. G. Kwon 《Proceedings of the American Mathematical Society》1996,124(5):1473-1480
If is a holomorphic self-map of the open unit disc and , then the following are equivalent. for all Bloch functions .
where is the hyperbolic derivative of : .
17.
Katsuhiko Matsuzaki 《Proceedings of the American Mathematical Society》2007,135(8):2573-2579
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 .
18.
David Harbater Leila Schneps 《Transactions of the American Mathematical Society》2000,352(7):3117-3148
Let denote the moduli space of Riemann spheres with ordered marked points. In this article we define the group of quasi-special symmetric outer automorphisms of the algebraic fundamental group for all to be the group of outer automorphisms respecting the conjugacy classes of the inertia subgroups of and commuting with the group of outer automorphisms of obtained by permuting the marked points. Our main result states that is isomorphic to the Grothendieck-Teichmüller group for all .
19.
Let T(Δ) and B(Δ) be the Teichmüller space and the infinitesimal Teichmüller space of the unit disk Δ respectively. In this paper, we show
that [ν]
B(Δ) being an infinitesimal Strebel point does not imply that [ν]
T(Δ) is a Strebel point, vice versa. As an application of our results, problems proposed by Yao are solved.
This work was supported by the National Natural Science Foundation of China (Grant No. 10571028) 相似文献
20.
李忠 《中国科学A辑(英文版)》2001,44(8):969-979
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