Related papers: Universal Teichm\"uller space in geometry and phys…

We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\"uller space, this semisimplicity…

A strong generalized topological space is an ordered pair $\mathbf{X}=\langle X, \mathcal{T}\rangle$ such that $X$ is a set and $\mathcal{T}$ is a collection of subsets of $X$ such that $\emptyset, X\in \mathcal{T}$ and $\mathcal{T}$ is…

The aim of these notes is to provide an introduction to Anti-de Sitter geometry, with special emphasis on dimension three and on the relations with Teichm\"uller theory, whose study has been initiated by the seminal paper of Geoffrey Mess…

This is a commentary on Teichm\"ullers' paper "Ver\"anderliche Riemannsche Fl\"achen" (Variable Riemann Surfaces), published in 1944. This paper is the last one that Teichm\"uller wrote on the problem of moduli. At most places the paper…

In this article, we derive estimates of Teichm\"uller modular forms, and associated invariants. Let $\mathcal{M}_{g}$ denote the moduli space of compact hyperbolic Riemann surfaces of genus $g\geq 2$, and let $\overline{M}_{g}$ be the…

Thurston's boundary to 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 Teichm\"uller type if it…

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…

We develop an analog of the notion of a character variety in the context of algebraic correspondences. It turns out that matings of certain Fuchsian groups and polynomials are contained in this ambient character variety. This gives rise to…

We study isometric maps between Teichm\"uller spaces and bounded symmetric domains in their intrinsic Kobayashi metric. From a complex analytic perspective, these two important classes of geometric spaces have several features in common but…

We propose an optimization algorithm for computing geodesics on the universal Teichm\"uller space T(1) in the Weil-Petersson ($W P$) metric. Another realization for T(1) is the space of planar shapes, modulo translation and scale, and thus…

We study the geometry of horospheres in Teichm\"uller space of Riemann surfaces of genus g with n punctures, where $3g-3+n\geq 2$. We show that every $C^1$-diffeomorphism of Teichm\"uller space to itself that preserves horospheres is an…

The Bers-Greenberg theorem tells that the Teichm\"{u}ller space of a Riemann surface with branch points (orbifold) depends only on the genus and the number of special points, but not on the particular ramification values. On the other hand,…

This paper is a comprehensive introduction to the results of [7]. It grew as an expanded version of a talk given at INdAM Meeting Complex and Symplectic Geometry, held at Cortona in June 12-18, 2016. It deals with the construction of the…

We consider classical Teichmuller theory and the geodesic flow on the cotangent bundle of the Teichmuller space. We show that the corresponding orbits provide a canonical description of certain (2+1) gravity systems in which a set of…

We study the Bers isomorphism between the Teichm\"uller space of the parabolic cyclic group and the universal Teichm\"uller curve. We prove that this is a group isomorphism and its derivative map gives a remarkable relation between Fourier…

In previous work it had been shown that the remarkable homogeneous space $M= \operatorname{Diff}(S^1)/\operatorname{PSL} (2,\Bbb{R})$ sits as a complex analytic and K\"ahler submanifold of the Universal Teichm\"uller Space. There is a…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm\"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics…

The problem of starlikeness of Teichmuller spaces in Bers' embedding was raised in 1974 and is solved (negatively) for Teichmuller spaces of sufficiently large dimensions. The original proof given by the author relies on the existence of…

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…