Related papers: Generalized stretch lines for surfaces with bounda…
We study Thurston's Lipschitz and curve metrics, as well as the arc metric on the Teichmueller space of one-hold tori equipped with complete hyperbolic metrics with boundary holonomy of fixed length. We construct natural Lipschitz maps…
We continue the study of the analogue of Thurston's metric on the Teichm{\"u}ller space of Euclidean triangle which was started by Saglam and Papadopoulos in [1].By direct calculation, we give explicit expressions of the distance function…
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…
The Teichm\"uller space $\mathcal{T}(\Sigma)$ of a surface $\Sigma$ is equipped with Thurston's asymmetric metric. Stretch lines are oriented geodesics for this metric on $\mathcal{T}(\Sigma)$. We give the asymptotic behavior of the lengths…
The Thurston metric on Teichmuller space, first introduced by W. P. Thurston is an asymmetric metric on Teichmuller space defined by $d_{Th}(X,Y) = \frac12 log\sup_{\alpha} \frac{l_{\alpha}(Y)}{l_{\alpha}(X)}$. This metric is geodesic, but…
In the Teichm\"uller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to…
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We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic metric on the same surface for which the lengths of all simple…
Let $X$ be an infinite geodesically complete hyperbolic surface which can be decomposed into geodesic pairs of pants. We introduce Thurston's boundary to the Teichm\"uller space $T(X)$ of the surface $X$ using the length spectrum analogous…
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…
We develop the notion of the active interval for a subsurface along a geodesic in the Thurston metric on Teichmuller space of a surface S. That is, for any geodesic in the Thurston metric and any subsurface R of S, we find an interval of…
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…
Thurston introduced in his seminal work an asymmetric metric on Teichm\"uller space by the ratio of simple closed curve length. In this paper, we generalize the idea and define an asymmetric metric on the space of unit-area flat metrics…
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…
We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent spheres based at any marked hyperbolic surface representing a…
For a compact surface $X_0$, Thurston introduced a compactification of its Teichm\"uller space $\mathcal T(X_0)$ by completing it with a boundary $\mathcal{PML}(X_0)$ consisting of projective measured geodesic laminations. We introduce a…
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…
These are notes on the hyperbolic geometry of surfaces, Teichm{\"u}ller spaces and Thurston's metric on these spaces. They are associated with lectures I gave at the Morningside Center of Mathematics of the Chinese Academy of Sciences in…
Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{H})$ is the set of asymptotic rays to the embedding of $T(\mathbb{H})$ in the space of geodesic currents; the boundary is identified with the projective bounded measured…
In this paper, we introduce an asymmetric metric on the space of marked Euclidean triangles, and we prove several properties of this metric, including two equivalent definitions of this metric, one of them comparing ratios of functions of…