A cofinite universal space for proper actions for mapping class groups (2008)
We prove that the mapping class group $\Gamma_{g,n}$ for surfaces of negative Euler characteristic has a cofinite universal space $\E$ for proper actions (the resulting quotient is a finite...
Understanding Weil-Petersson curvature (2008)
A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichm\"{u}ller theory are provided. A report is presented on the program to describe an intrinsic geometry with...
The Weil-Petersson metric geometry (2007)
A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the...
Topological dynamics of the Weil-Petersson geodesic flow (2007)
Pollicott, Mark, Weiss, Howard, Wolpert, Scott A.
We prove topological transitivity for the Weil Petersson geodesic flow for two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that exploits the density of...
Extension of the Weil-Petersson connection (2007)
Convexity properties of Weil-Petersson geodesics on the Teichm\"{u}ller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection...
Weil-Petersson Metric Geometry Quick Overview (2007)
A quick overview is provided on the current development of the WP metric geometry.
Grafting hyperbolic metrics and Eisenstein series (2007)
Obitsu, Kunio, Wolpert, Scott A.
The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(\zeta;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for...
Behavior of geodesic-length functions on Teichmueller space (2007)
Let $\mathcal T$ be the Teichm\"{u}ller space of marked genus $g$, $n$ punctured Riemann surfaces with its bordification $\Tbar$ the {\em augmented Teichm\"{u}ller space} of marked Riemann surfaces...
Cusps and the family hyperbolic metric (2005)
The hyperbolic metric for the punctured unit disc in the Euclidean plane is singular at the origin. A renormalization of the metric at the origin is provided by the Euclidean metric. For Riemann...
Weil-Petersson perspectives (2005)
We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichm\"{u}ller spaces. For recent progress on and the understanding of infinite dimensional...
Convexity of geodesic-length functions: a reprise (2005)
New results on the convexity of geodesic-length functions on Teichm\"{u}ller space are presented. A formula for the Hessian of geodesic-length is presented. New bounds for the gradient and Hessian of...
Geometry of the Weil-Petersson completion of Teichm\"uller space (2005)
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...
Semiclassical limits for the hyperbolic plane (2001)
We study the concentration properties of high-energy eigenfunctions for the Laplace-Beltrami operator of the hyperbolic plane with special consideration of automorphic eigenfunctions. At the center...
The Weil-Petersson metric for Teichmueller space and the Jenkins-Strebel differentials / (1976)
Thesis (Ph. D.)--Dept. of Mathematics, Stanford University.