Related papers: Bers isomorphism on the universal Teichm\"uller cu…
We consider a quotient space of the Bers boundary of Teichm\"{u}ller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space into a point. This reduced Bers boundary turns out to be independent…
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…
We construct an Ahlfors-Bers complex analytic model for the Teichm\"uller space of the universal hyperbolic lamination (also known as Sullivan's Teichm\"uller space) and the renormalized Weil-Petersson metric on it as an extension of 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 consider the group of sense-preserving diffeomorphisms $\Diff S^1$ of the unit circle and its central extension, the Virasoro-Bott group, with their respective horizontal distributions chosen to be Ehresmann connections with respect to a…
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…
We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The…
Let $\Sigma$ be a Riemann surface of genus $g$ bordered by $n$ curves homeomorphic to the circle $\mathbb{S}^1$, and assume that $2g+2-n>0$. For such bordered Riemann surfaces, the authors have previously defined a Teichm\"uller space which…
Based on the quasiconformal theory of the universal Teichm\"uller space, we introduce the Teichm\"uller space of diffeomorphisms of the unit circle with $\alpha$-H\"older continuous derivatives as a subspace of the universal Teichm\"uller…
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…
We develop a natural and geometric way to realize the hyperbolic plane as the moduli space of marked genus 1 Riemann surfaces. To do so, a metric is defined on the Teichm\"uller space of the torus, inspired by Thurston's Lipschitz metric…
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…
Similarly to the Bers simultaneous uniformization, the product of the $p$-Weil-Petersson Teichm\"uller spaces for $p \geq 1$ provides the coordinates for the space of $p$-Weil-Petersson embeddings $\gamma$ of the real line $\mathbb R$ into…
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…
A cyclic cover of the complex projective line branched at four appropriate points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding…
A Teichm\"uller curve is an algebraic and isometric immersion of an algebraic curve into the moduli space of Riemann surfaces. We give the first explicit algebraic models of Teichm\"uller curves of positive genus. Our methods are based on…
We interpolate a new family of Teichm\"uller spaces $T_{\sharp}^X$ between the universal Teichm\"uller space $T$ and its little subspace $T_0$, which we call the Teichm\"uller space of piecewise symmetric homeomorphisms. This is defined by…
We consider deformations of a group of circle diffeomorphisms with H\"older continuous derivatives in the framework of quasiconformal Teichm\"uller theory and show certain rigidity under conjugation by symmetric homeomorphisms of the…
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…
The paper presents some recent results on the Weil-Petersson geometry theory of the universal Teichm\"uller space, a topic which is important in Teichm\"uller theory and has wide applications to various areas such as mathematical physics,…