On Limits of Quasi-Conformal Deformations of Kleinian Groups.
On locally biholomorphic mappings from multi-connected onto simply connected domains
We continue E. Ligocka's investigations concerning the existence of m-valent locally biholomorphic mappings from multi-connected onto simply connected domains. We decrease the constant m, and also give the minimum of m in the case of mappings from a wide class of domains onto the complex plane ℂ.
On locally biholomorphic surjective mappings
We prove that each open Riemann surface can be locally biholomorphically (locally univalently) mapped onto the whole complex plane. We also study finite-to-one locally biholomorphic mappings onto the unit disc. Finally, we investigate surjective biholomorphic mappings from Cartesian products of domains.
On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms
The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain...
On monodromy map.
On ovals on Riemann surfaces.
We prove that k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus g have at most 2g - 2 + 2r - 3(9 - k) ovals in total, where r is the smallest positive integer for which k ≤ 2r - 1. Furthermore we prove that for arbitrary k ≥ 9 this bound is sharp for infinitely many values of g.
On -hyperelliptic involutions of Riemann surfaces.
On pairs of closed geodesics on hyperbolic surfaces
In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups . This links the intersection angles and common perpendiculars of pairs of closed geodesics on with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.
On p-hyperellipticity of doubly symmetric Riemann surfaces.
Studying commuting symmetries of p-hyperelliptic Riemann surfaces, Bujalance and Costa found in [3] upper bounds for the degree of hyperellipticity of the product of commuting (M - q)- and (M - q')-symmetries, depending on their separabilities. Here, we find necessary and sufficient conditions for an integer p to be the degree of hyperellipticity of the product of two such symmetries, taking into account their separabilities. We also give some results concerning the existence and uniqueness of symmetries...
On pq-hyperelliptic Riemann surfaces
A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ is an orbifold of genus p. If in addition X admits a q-hypereliptic involution then we say that X is pq-hyperelliptic. We give a necessary and sufficient condition on p,q and g for existence of a pq-hyperelliptic Riemann surface of genus g. Moreover we give some conditions under which p- and q-hyperelliptic involutions of a pq-hyperelliptic...
On quasiconformal mappings of open Riemann surfaces.
On ramifications divisors of functions in a punctured compact Riemann surface.
Let ν be a compact Riemann surface and ν' be the complement in ν of a nonvoid finite subset. Let M(ν') be the field of meromorphic functions in ν'. In this paper we study the ramification divisors of the functions in M(ν') which have exponential singularities of finite degree at the points of ν-ν', and one proves, for instance, that if a function in M(ν') belongs to the subfield generated by the functions of this type, and has a finite ramification divisor, it also has a finite divisor. It is also...
On rotation-automorphic functions.
On Schottky groups with automorphisms.
On soluble groups of automorphisms of nonorientable Klein surfaces
We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.
On Spaces of Kleinian Groups
On supersoluble groups acting on Klein surfaces.
On Teichmüller modular forms.
On the Analytic Continuation of Rank One Eisenstein Series.
On the analytic solution of the equation of fifth degree