A bound for reflections across Jordan curves.
A cellular parametrization for closed surfaces with a distinguished point.
A characterization of Fuchsian groups acting on complex hyperbolic spaces
Let be a non-elementary complex hyperbolic Kleinian group. If preserves a complex line, then is -Fuchsian; if preserves a Lagrangian plane, then is -Fuchsian; is Fuchsian if is either -Fuchsian or -Fuchsian. In this paper, we prove that if the traces of all elements in are real, then is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an application...
A characterization of short curves of a Teichmüller geodesic.
A construction of the Deligne-Mumford orbifold
A criterion for the existence of a flat connection on a parabolic vector bundle.
A distortion theorem for bounded univalent functions.
A family of M-surfaces whose automorphism groups act transitively on the mirrors.
Let X be a compact Riemmann surface of genus g > 1. A symmetry T of X is an anticonformal involution. The fixed point set of T is a disjoint union of simple closed curves, each of which is called a mirror of T. If T fixes g +1 mirrors then it is called an M-symmetry and X is called an M-surface. If X admits an automorphism of order g + 1 which cyclically permutes the mirrors of T then we shall call X an M-surface with the M-property. In this paper we investigate those M-surfaces with the...
A foliation of Teichmüller space by twist invariant disks.
A footnote to the Poincaré complete reducibility theorem.
Poincaré's work on the reduction of Abelian integrals contains implicitly an algorithm for the expression of a theta function as a sum of products of theta functions of fewer variables in the presence of reduction. The aim of this paper is to give explicit formulations and reasonably complete proofs of Poincaré's results.
A Fuchsian group proof of the hyperellipticity of Riemann surfaces of genus 2.
A fundamental domain for the modular group of Riemann surfaces of type .
A gallery of iterated correspondences.
A generalisation of Teichmüller space in the hermitian context
A generalization of Jørgensen's inequality to infinite dimension.
A holomorphic correspondence at the boundary of the Klein combination locus
We investigate an explicit holomorphic correspondence on the Riemann sphere with striking dynamical behaviour: the limit set is a fractal resembling the one-skeleton of a tetrahedron and on each component of the complement of this set the correspondence behaves like a Fuchsian group.
A Kleinian group with contractible quotient not simply connected at infinity.
A Modular Group and Riemann Surfaces of Genus 2.
A natural graded Lie algebra sheaf over Riemann surfaces
A new characterization of Gromov hyperbolicity for negatively curved surfaces.
In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a simple closed geodesic. This result is, in fact, a new characterization of Gromov hyperbolicity for Riemann surfaces.