相关论文: Extremal length estimates and product regions in T…
We consider some metrics and weak metrics defined on the Teichmueller 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…
Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…
There are several Teichm\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal…
We show that the length spectrum metric on Teichm\"uller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichm\"uller space with quasiconformal and the…
We prove that the Teichm\"uller space of surfaces with given boundary lengths equipped with the arc metric (resp. the Teichm\"uller metric) is almost isometric to the Teichm\"uller space of punctured surfaces equipped with the Thurston…
The Teichm\"{u}ller curve is the fiber space over Teichm\"{u}ller space of closed Riemann surfaces, where the fiber over a point in Teichm\"{u}ller space is the underlying surface. We derive formulas for sectional curvatures on the…
Considering the Teichm\"uller space of a surface equipped with Thurston's Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and that the closest-point…
We define and study metrics and weak metrics on the Teichmueller 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…
We show that the Teichm\"uller space of a surface without boundary and with punctures, equipped with Thurston's metric is the limit (in an appropriate sense) of Teichm\"uller spaces of surfaces with boundary, equipped with their arc…
We study the asymptotic behavior of extremal length along Teichm\"uller rays. Specifically, we determine the limit of extremal length along a Teichm\"uller ray and obtain an explicit expression for this limit, which complements a related…
Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann…
We prove that the every quasi-isometry of Teichm\"uller space equipped with the Teichm\"uller metric is a bounded distance from an isometry of Teichm\"uller space. That is, Teichm\"uller space is quasi-isometrically rigid.
This paper is devoted to study of transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptotic behavior of the Gromov product in hyperbolic spaces. We…
Over the past two decades the theory of the Weil-Petersson metric has been extended to general Teichm\"uller spaces of infinite type, including for example the universal Teichm\"uller space. In this paper we give a survey of the main…
In this paper we explore the idea that Teichm\"uller space is hyperbolic "on average." Our approach focuses on studying the geometry of geodesics which spend a definite proportion of time in some thick part of Teichm\"uller space. We…
We highlight several analogies between the Finsler (infinitesimal) properties of Teichm\"uller's metric and Thurston's asymmetric metric on Teichm\"uller space. Thurston defined his asymmetric metric in analogy with Teichm\"ullers' metric,…
This paper is a survey about the Thurston metric on the Teichm\"uller space. The central issue is the constructions of extremal Lipschitz maps between hyperbolic surfaces. We review several constructions, including the original work of…
We develop a natural and geometric way to realize the hyperbolic plane as the moduli space of marked genus 1 Riemann surfaces. To do so, a metric is defined on the Teichm\"uller space of the torus, inspired by Thurston's Lipschitz metric…
We determine the asymptotic behaviour of extremal length along arbitrary Teichm\"uller rays. This allows us to calculate the endpoint in the Gardiner-Masur boundary of any Teichm\"uller ray. We give a proof that this compactification is the…
Given a surface of infinite topological type, there are several Teichm\"uller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the…