Length spectra and the Teichmüller metric for surfaces with boundary
نویسنده
چکیده
We consider some metrics and weak metrics defined on the Teichmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call “ε0-relative ǫ-thick parts”, and whose definition depends on the choice of some positive constants ε0 and ǫ. Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs. AMS Mathematics Subject Classification: 32G15 ; 30F30 ; 30F60.
منابع مشابه
Thurston’s Metric on Teichmüller Space and Isomorphisms between Fuchsian Groups
The aim of this paper is to relate Thurston’s metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will give a new formula for Thurston’s asymmetric metric for surfaces with punctures. We also update some results of Sorvali on boundary isomorphisms of Fuchsian groups. AMS Mathematics Subject Classification: 32G15 ; 30F...
متن کاملGeodesic Length Functions and Teichmüller Spaces
Abstract Given a compact orientable surface with finitely many punctures Σ, let S(Σ) be the set of isotopy classes of essential unoriented simple closed curves in Σ. We determine a complete set of relations for a function from S(Σ) to R to be the geodesic length function of a hyperbolic metric with geodesic boundary and cusp ends on Σ. As a consequence, the Teichmüller space of hyperbolic metri...
متن کاملOn Length Spectrum Metrics and Weak Metrics on Teichmüller Spaces of Surfaces with Boundary
We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call ε0-relative ǫ-thick parts...
متن کاملAsymptotic Flatness of the Weil–Petersson Metric on Teichmüller Space
In this paper, we show that there is no negative upper bound for the sectional curvature of Teichmüller space of Riemann surfaces with the Weil–Petersson metric. Mathematics Subject Classifications (2000). 32G15, 53C21, 30F60.
متن کاملThe Universal Properties of Teichmüller Spaces
We discuss universal properties of general Teichmüller spaces. Our topics include the Teichmüller metric and the Kobayashi metric, extremality and unique extremality of quasiconformal mappings, biholomorphic maps between Teichmüller space, earthquakes and Thurston boundary.
متن کامل