Length functions and parameterizations of Teichmüller space for surfaces with cusps.
Lengths of simple loops on surfaces with hyperbolic metrics.
Limit points of lines of minima in Thurston's boundary of Teichmüller space.
Methodik der stetigen Deformation von zweiblättrigen Riemann'schen Flächen [Book]
Modules des surfaces de Riemann
Multiple prime covers of the riemann sphere
A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.
Navigating moduli space with complex twists
We discuss a common framework for studying twists of Riemann surfaces coming from earthquakes, Teichmüller theory and Schiffer variations, and use it to analyze geodesics in the moduli space of isoperiodic 1-forms.
Nielsen's theorem and the super-Teichmüller space
Non-rectifiable limit sets of dimension one.
We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' beta's, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability and (3)...
Non-uniqueness of geodesics in infinite-dimensional Teichmüller spaces. II.
On a distance defined by the length spectrum on Teichmüller space.
On Teichmüller modular forms.
On the Bers fiber spaces.
On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.
On the shape of Bers-Maskit slices.
On the tangent space to the universal Teichmüller space.
Orbifold Riemann surfaces and the Yang-Mills-Higgs equations
Pleating coordinates for the Earle embedding
Pointed -surfaces
Let be a Riemann surface. Let be the -dimensional hyperbolic space and let be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping . If is a convex immersion, and if is its exterior normal vector field, we define the Gauss lifting, , of by . Let be the Gauss-Minkowski mapping. A solution to the Plateau problem is a convex immersion of constant Gaussian curvature equal to such that the Gauss lifting is complete and . In this paper, we show...
Polyhedral Realization of a Thurston Compactification
Let be the connected sum of three real projective planes. We realize the Thurston compactification of the Teichmüller space as a simplex in .