Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebe...Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebel point τ ∈ T(S), there are infinitely many aeodesic discs containina [0] and τ.展开更多
The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT（X） is proved. Then, the notion of angles between two g...The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT（X） is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller 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.展开更多
LET[μ] be a point in a Teichmuller space T（Γ） and [μ]≠[0]. When T（Γ） is finite-di-mensional, the extremal Beltrami differential in [μ]is unique and the geodesic segment α:[tμ<sub>0</sub>] （0≤...LET[μ] be a point in a Teichmuller space T（Γ） and [μ]≠[0]. When T（Γ） is finite-di-mensional, the extremal Beltrami differential in [μ]is unique and the geodesic segment α:[tμ<sub>0</sub>] （0≤t≤1） is the unique geodesic segment joining [0] and [μ], where μ<sub>0</sub> is the uniqueextremal Beltrami differential in [μ]. However, when T（Γ） is infinite-dimensional, [μ]展开更多
基金supported by the 973-Project Foundation(Grant No.TG199075105)the Research Fund for Doctoral Program of Higher Education,
文摘Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebel point τ ∈ T(S), there are infinitely many aeodesic discs containina [0] and τ.
基金supported by National Natural Science Foundation of China(11371045,11301248)
文摘The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT（X） is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller 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.
文摘LET[μ] be a point in a Teichmuller space T（Γ） and [μ]≠[0]. When T（Γ） is finite-di-mensional, the extremal Beltrami differential in [μ]is unique and the geodesic segment α:[tμ<sub>0</sub>] （0≤t≤1） is the unique geodesic segment joining [0] and [μ], where μ<sub>0</sub> is the uniqueextremal Beltrami differential in [μ]. However, when T（Γ） is infinite-dimensional, [μ]
