Let $ S_ {g, n} $ be a surface of genus $ g $ with $ n $ marked points. Let $ X $ be a
complete hyperbolic metric on $ S_ {g, n} $ with $ n $ cusps. Every isotopy class $[\gamma] …

Let Σ Σ be a hyperbolic surface. We study the set of curves on Σ Σ of a given type, ie in the
mapping class group orbit of some fixed but otherwise arbitrary\gamma_0 γ 0. For example …

We study the Weyl chamber length compactification both of the Hitchin and of the maximal
character varieties and determine therein an open set of discontinuity for the action of the …

Many natural real-valued functions of closed curves are known to extend continuously to the
larger space of geodesic currents. For instance, the extension of length with respect to a …

We find a compactification of the SL (3, R)-Hitchin component by studying the degeneration
of the Blaschke metrics on the associated equivariant affine spheres. In the process, we …

In this paper we prove that the space of flat metrics (nonpositively curved Euclidean cone
metrics) on a closed, oriented surface is marked-length-spectrally rigid. In other words, two …

Every geodesic current on a hyperbolic surface has an associated dual space. If the current
is a lamination, this dual embeds isometrically into a real tree. We show that, in general, the …

This chapter is a survey about the Thurston metric on the Teichmüller space. The central
issue is the construction of extremal Lipschitz maps between hyperbolic surfaces. We review …

We show that a Hitchin representation is determined by the spectral radii of the images of
simple, non-separating closed curves. As a consequence, we classify isometries of the …

In this paper, we study the asymptotic behavior of Teichmüller geodesic rays in the Gardiner–
Masur compactification. We will observe that any Teichmüller geodesic ray converges in the …