Related papers: Caratheodory metrics on Teichmuller spaces

We study the metric and topological properties of the space $\mathscr{D}(G)$ of left-invariant hyperbolic pseudometrics on the non-elementary hyperbolic group $G$ that are quasi-isometric to a word metric, up to rough similarity. This space…

We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the Teichm\"uller metric is approximated up…

We observe Thurston's asymmetric metric on Teichm\"uller space may be expressed in terms of the H\"older regularity of boundary maps. We then associate $2$-dimensional stratified loci in $\mathbb{RP}^{n-1}$ to $\text{PSL}_n(\mathbb{R})$…

We study Carath\'eodory convergence for open, simply connected surfaces spread over the sphere and, in particular, provide examples demonstrating that in the Speiser class the conformal type can change when two singular values collide.

We start the investigation of immersions $\Psi$ of a simply connected domain $D$ into three dimensional Euclidean space $R^3$, which have constant mean curvature (CMC-immersions), and allow for a group of automorphisms of $D$ which leave…

We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert…

In this note we show that for any hyperbolic surface S, the number of geodesics of length bounded above by L in the mapping class group orbit of a fixed closed geodesic with a single double point is asymptotic to L raised to the dimension…

Let $S$ be a set of $n$ points in 3-dimensional space. A tetrahedralization $\mathcal{T}$ of $S$ is a set of interior disjoint tetrahedra with vertices on $S$, not containing points of $S$ in their interior, and such that their union is the…

In this paper, the Teichm{\"u}ller spaces of surfaces appear from two points of views: the conformal category and the hyperbolic category. In contrast to the case of surfaces of topologically finite type, the Teichm{\"u}ller spaces…

In this paper, we study the existence of twisted constant scalar curvature K\"{a}hler (cscK) metrics and non-existence of coupled cscK metrics on minimal ruled surfaces over a Riemann surface of genus $2$. Moreover, we give a bound for the…

There exists on each Teichm\"uller space $T_g$ (comprising compact Riemann surfaces of genus $g$), a natural sequence of determinant (of cohomology) line bundles, $DET_n$, related to each other via certain ``Mumford isomorphisms''. There is…

We prove that the pressure metric on the Teichm\"uller space of a bordered surface is incomplete and its partial completion can be given by the moduli space of metric graphs for a fat graph associated to the same bordered surface equipped…

We construct complete Riemannian metrics to show that the total space of tangent bundles of orientable closed surfaces (except torus) admits complete uniformly PSC-metrics. It gives a partial positive answer to one of Gromov's question.

For each integer $D \geq 5$ with $D \equiv 0$ or $1 \bmod 4$, the Weierstrass curve $W_D$ is an algebraic curve and a finite volume hyperbolic orbifold which admits an algebraic and isometric immersion into the moduli space of genus two…

For any analytically finite Riemann surface, the Teichm\"uller modular group is countable, but it is not easy to find an analytically infinite Riemann surface for which the Teichm\"uller modular group is countable. In this paper, we show…

We introduce a function model for the Teichm\"uller space of a closed hyperbolic Riemann surface. Then we introduce a new metric by using the maximum norm on the function space on the Teichm\"uller space. We prove that the identity map from…

This work is motivated by two central questions in the birational geometry of moduli spaces of curves -- Fulton's conjecture and the effective cone of $\bar M_g$. We study the algebro-geometric aspect of Teichmuller curves parameterizing…

We use PDE methods as developed for the Liouville equation to study the existence of conformal metrics with prescribed singularities on surfaces with boundary, the boundary condition being constant geodesic curvature. Our first result shows…

Thurston boundary of the universal Teichm\"uller space $T(\mathbb{D})$ is the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of $\mathbb{D}$. A geodesic ray in $T(\mathbb{D})$ is of generalized Teichm\"uller type…

In this paper, we introduce a new asymmetric weak metric on the Teichm{\"u}ller space of a closed orientable surface with (possibly empty) punctures.This new metric, which we call the Teichm{\"u}ller-Randers metric, is an asymmetric…