A better proof of the Goldman-Parker conjecture.
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 note on isolated points in the branch locus of the moduli space of compact Riemann surfaces.
A Note on the Amenable Subgroups of PSL (2, R).
A rigidity theorem for Möbius groups.
A Symbolic Dynamics for Geodesics on Punctured Riemann Surfaces.
A uniformly quasiconformal group not isomorphic to a Möbius group.
Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
All Two-Gnerator Fuchsian Group.
An algorithm for finding the Veech group of an origami.
An application of metric diophantine approximation in hyperbolic space to quadratic forms.
For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...
An example of an arithmetic Fuchsian group.
Application aux fonctions circulaires et aux fonctions elliptiques d'une méthode générale de détermination des fonctions dont on donne le groupe des substitutions
Application of Hoare's theorem to symmetries of Riemann surfaces.
Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps
We consider a large class of non compact hyperbolic manifolds with cusps and we prove that the winding process generated by a closed -form supported on a neighborhood of a cusp , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp and the Poincaré exponent of . No assumption on the value of is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.
Automorphism groups of orientable elliptic-hyperelliptic Klein surfaces.
Automorphismen und Erzeugende für Gruppen mit einer definierenden Relation.
Beiträge zur geometrischen Interpretation binärer Formen
Big groups of automorphisms of some Klein surfaces.
Sea Xp una superficie de Klein compacta con borde de gen algebraico p ≥ 2. Se sabe que si G es un grupo de automorfismos de Xp entonces |G| ≤ 12(p- 1). Se dice que G es un grupo grande de gen p si |G| > 4(p -1). En el presente artículo se halla una familia de enteros p para los que el único grupo grande de gen p son los grupos diédricos. Esto significa que, en términos del gen real introducido por C. L. May, para tales valores de p no existen grupos grandes de gen real p.
Character theory of symmetric groups, analysis of long relators, and random walks.