Related papers: Weil-Petersson Teichm\"uller space

Using the identification of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$ with the Teichm\"uller space of flat $n$-tori of unit volume, we explore several metrics and compactifications of these spaces, drawing inspiration…

This is a mathematical commentary on Teichm{\"u}ller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl{\"a}chen'' (Determination of extremal quasiconformal maps of closed oriented…

We prove that the universal Teichmuller space T(1) carries a new structure of a complex Hilbert manifold. We show that the connected component of the identity of T(1), the Hilbert submanifold T_{0}(1), is a topological group. We define a…

We extend Velling's approach and prove that the second variation of the spherical areas of a family of domains defines a Hermitian metric on the universal Teichmuller curve, whose pull back to Diff+(S^1)/S^1 coincides with the Kirillov…

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 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…

Fix a number $g>1$, let $S$ be a close surface of genus $g$, and $Teich(S)$ be the Teichm\"uller space of $S$ endowed with the Weil-Petersson metric. In this paper we show that the Riemannian sectional curvature operator of $Teich(S)$ is…

We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichm\"{u}ller space of a punctured surface. Via the embedding, the Weil-Petersson…

For $s >\frac{3}{2}$, the group of Sobolev class s diffeomorphisms of the circle is a smooth manifold modeled on the space of Sobolev class s sections of the tangent bundle of the circle. It is a topological group in the sense that…

We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2). Our method follows Ivanov's proof of the Royden's analogous…

We introduce and the study the space of homeomorphisms of the circle (up to M\"obius transformations) which are in $\ell^2$ with respect to modular coordinates called diamond shears along the edges of the Farey tessellation. Diamond shears…

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…

Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…

The Bers embedding of theTeichm\"uller space is a homeomorphism into the Banach space of certain holomorphic automorphic forms. For a subspace of the universal Teichm\"uller space and its corresponding Banach subspace, we consider whether…

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…

This is the author's Ph.D. thesis, submitted to the University of Leipzig. It deals with the $L^2$ Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold. The main body of the…

We apply the methods of simultaneous uniformization and composition operators on Besov spaces to the Teichm\"uller space $T^Z$ of circle diffeomorphisms with Zygmund continuous derivatives. As consequences, we obtain the following: (1) a…

We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichm\"uller space. We sketch a collection of results by other authors and then proceed to develop the properties of…

This thesis results from an intensive study on the canonical metrics on the Teichm\"{u}ller spaces and the moduli spaces of Riemann surfaces. There are several renowned classical metrics on $T_g$ and $\mathcal{M}_g$, including the…

This is a commentary on Teichm{\"u}ller's paper Unter-suchungen{\"u}ber konforme und quasikonforme Abbildungen (Inves-tigations on conformal and quasiconformal mappings) published in 1938. The paper contains fundamental results in conformal…