共查询到20条相似文献,搜索用时 15 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.
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
3.
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
4.
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
5.
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
6.
Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces 下载免费PDF全文
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. 相似文献
8.
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
9.
A.Turan Gǖrkanli 《数学物理学报(B辑英文版)》2003,23(4)
Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1(G) to A is algebrically isomorphic and homeomorphic to A. 相似文献
10.
《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
11.
Xiaobo Liu 《数学学报(英文版)》2012,28(4):759-770
An earlier article [Bonahon, F., Liu, X. B.: Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms. Geom. Topol., 11, 889-937 (2007)] introduced new invariants for pseudo-Anosov diffeomorphisms of surface, based on the representation theory of the quantum Teichmu¨ller space. We explicitly compute these quantum hyperbolic invariants in the case of the 1-puncture torus and the 4-puncture sphere. 相似文献
12.
This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed. 相似文献
13.
Let R *θG be the skew group ring with a F.C group G and the group homom-rphismθfrom G to Aut(R), the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R*θG will be Noetherian is given, which generalizes the results of I.G. connel. 相似文献
14.
Kobayashi's and Teichm¨uller's Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms 下载免费PDF全文
《数学学报(英文版)》2020,(3)
Given a modulus of continuity ω,we consider the Teichmuller space TC~(1+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 C~1 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. 相似文献
15.
Let Г be a Fuchsian group acting on the upper half plane H. We denote byBel(Г) the set of all Beltrami differentials of Г on H with L~∞-norms less than 1.For each μ∈Bel(Г) there exists a uniquely determiued quasiconformal mapping f_μ:H→H with the complex dilatation μ, which keeps 0,1 and ∞ fixed. Two elementsμ_1 and μ_2 of Bel(Г) are said to be equivalent each other if f_(μ1)|R coincides withf_(μ2) |R. Then the Teichmuller space of Г is defined to be the set of all equivalenceclasses of elements in Bel(Г). 相似文献
16.
《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
17.
Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP. 相似文献
18.
Let G be a finite group and S a subset of G.We define the Cayley digraphX=X(C,S)of G with respect to S bywhere V(X)and E(X)are the vertex-and edge-sets of X,respectively.S is saidto be a CI—subset of G if any graphisomorphism X(G,S)≌X(G,T),where TG,implies that there exists a group automorphism α∈ Aut G such that S~α=T. 相似文献
19.
A. Turan Gürkanl 《数学物理学报(B辑英文版)》2007,27(1):107-116
Let G be a locally compact abelian group. The main purpose of this article is to find the space of multipliers from the Lorentz space L(p1, q1)(G) to L(p21,q21)(G). For this reason, the authors define the space Ap1,q1p2,q2(G), discuss its properties and prove that the space of multipliers from L(p1,q1)(G) to L(p21,q21)(G) is isometrically isomorphic to the dual of Ap1,q1p2q2(G). 相似文献
20.
Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms 下载免费PDF全文
Yun Ping JIANG 《数学学报(英文版)》2020,36(3):245-272
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. 相似文献