On the asymptotic boundary paths of analytic functions.
On the automorphism group of a toroidal hypermap
On the Bers fiber spaces.
On the connectedness of the locus of real Riemann surfaces.
On the Density of Strebel Differentials.
On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.
On the dimension of limit sets of geometrically finite Möbius groups.
On the disc theorem
Ahlfors' disc theorem for Riemann covering surfaces is extended to normally exhaustible Klein coverings.
On the dynamics of pseudo-Anosov homeomorphisms on representation varieties of surface groups.
On the existence of Weierstrass points whose first non-gaps are five.
On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.
A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs...
On the finite blocking property
A planar polygonal billiard is said to have the finite blocking property if for every pair of points in there exists a finite number of “blocking” points such that every billiard trajectory from to meets one of the ’s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces....
On the Green's Fundamental Domain.
On the Homeotopy Groups of Surfaces.
On the Hyperbolicity of Certain Planar Domains.
On the ideal triangulation graph of a punctured surface
We study the ideal triangulation graph of an oriented punctured surface of finite type. We show that if is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of into the simplicial automorphism group of is an isomorphism. We also show that the graph of such a surface , equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punctured...
On the infinite volume Hecke surfaces
On the inner parts of certain analytic functions
On the Isomorphism Theorem for Kleinian Groups.
On the Kähler form of the moduli space of once punctured tori.