We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi＇s metric and Teichmuller＇s metric coincide with each other on the Teichmfiller space of symmetric circle homeomorphisms.
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
An earlier article [Bonahon, F., Liu, X. B.： Representations of the quantum Teichmfiller space and invariants of surface diffeomorphisms. Geom. Topol., 11, 889-937 （2007）] introduced new invariants for pseudo-Anoso...An earlier article [Bonahon, F., Liu, X. B.： Representations of the quantum Teichmfiller 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 Teichmiiller space. We explicitly compute these quantum hyperbolic invariants in the case of the 1-puncture torus and the 4-puncture sphere.展开更多
文摘We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi＇s metric and Teichmuller＇s metric coincide with each other on the Teichmfiller space of symmetric circle homeomorphisms.
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.
基金Partially supported by NSF grant DMS-0103511 at the University of Southern California
文摘An earlier article [Bonahon, F., Liu, X. B.： Representations of the quantum Teichmfiller 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 Teichmiiller space. We explicitly compute these quantum hyperbolic invariants in the case of the 1-puncture torus and the 4-puncture sphere.
