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 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 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 Modular Group and Riemann Surfaces of Genus 2.
A pseudo-trigonometry related to Ptolemy's theorem and the hyperbolic geometry of punctured spheres
A hyperbolic geodesic joining two punctures on a Riemann surface has infinite length. To obtain a useful distance-like quantity we define a finite pseudo-length of such a geodesic in terms of the hyperbolic length of its surrounding geodesic loop. There is a well defined angle between two geodesics meeting at a puncture, and our pseudo-trigonometry connects these angles with pseudo-lengths. We state and prove a theorem resembling Ptolemy's classical theorem on cyclic quadrilaterals and three general...
A remark on degenerate groups.
A scattering theory for automorphic functions
Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
All Two-Gnerator Fuchsian Group.
Almost automorphic solutions to some differential equations in Banach spaces.
Amenability, Poincaré series and quasiconformal maps.
An algorithm for finding the Veech group of an origami.
An elementary formula for the Fenchel-Nielsen twist.
An example of an arithmetic Fuchsian group.
An integral involving the generalized zeta function.
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
Application aux fonctions circulaires et aux fonctions elliptiques d'une méthode générale de détermination des fonctions dont on donne le groupe des substitutions