A Weierstrass-type representation for harmonic maps from Riemann surfaces to general Lie groups.
A4, A5, S4 and S5 of Schottky type.
Let H be a group of conformal automorphisms of a closed Riemann surface S, isomorphic to either of the alternating groups A4 or A5 or the symmetric groups S4 or S5. We provide necessary and sufficient conditions for the existence of a Schottky uniformization of S for which H lifts. In particular, togheter with the previous works in Hidalgo (1994,1999), we exhaust the list of finite groups of Möbius transformations of Schottky type.
Abelian coverings, Poincaré exponent of convergence and holomorphic deformations.
Addendum to: A foliation of Teichmüller space by twist invariant disks.
Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
Ahlfors-Schwarz lemma and curvature
Algebraic and geometric convergence of Kleinian groups.
Algebraic properties of mapping class groups of surfaces
Algebraische Funktionen mit Polen in spezieller Lage.
Algebras of differentiable functions on Riemann surfaces
La structure d’une variété indéfiniment différentiable est complètement caractérisée par l’algèbre des fonctions indéfiniment différentiables sur . Pour des surfaces de Riemann il n’y a pas, en général, une algèbre caractérisante canonique de fonctions globalement définies. Dans ce travail l’on définit une classe dénombrable de telles algèbres. Ces algèbres sont des analogues, pour les surfaces de Riemann, des algèbres définies pour le plan par les auteurs dans “Algebras of differentiable functions...
All Two-Gnerator Fuchsian Group.
Almost Abelian regular dessins d'enfants
A regular dessin d'enfant, in this paper, will be a pair (S,β), where S is a closed Riemann surface and β: S → ℂ̂ is a regular branched cover whose branch values are contained in the set {∞,0,1}. Let Aut(S,β) be the group of automorphisms of (S,β), that is, the deck group of β. If Aut(S,β) is Abelian, then it is known that (S,β) can be defined over ℚ. We prove that, if A is an Abelian group and Aut(S,β) ≅ A ⋊ ℤ₂, then (S,β) is also definable over ℚ. Moreover, if A ≅ ℤₙ, then we provide explicitly...
Almost automorphic solutions to some differential equations in Banach spaces.
Amenability, Poincaré series and quasiconformal maps.
Amenable coverings of complex manifolds and holomorphic probalitiy measures.
An algorithm for finding the Veech group of an origami.
An Algorithm To Compute Odd Orders and Ramification Indices of Cyclic Actions on Compact Surfaces.
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 earthquake version of the Jackson-Zygmund theorem.
An elementary formula for the Fenchel-Nielsen twist.