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Maximal real Schottky groups.

Rubén A. Hidalgo (2004)

Revista Matemática Iberoamericana

Let S be a real closed Riemann surfaces together a reflection τ : S ---> S, that is, an anticonformal involution with fixed points. A well known fact due to C. L. May asserts that the group K(S, τ), consisting on all automorphisms ...

Measured geodesic laminations in Flatland

Thomas Morzadec (2012/2014)

Séminaire de théorie spectrale et géométrie

Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure (that is a singular flat surface with holonomy { ± Id } ), called flat laminations, and we define transverse measures on flat laminations similar to transverse measures on hyperbolic laminations, taking into account that the images of the leaves of a flat lamination are in...

Metabelian groups acting on compact Riemann surfaces.

G. Gromadzki (1995)

Revista Matemática de la Universidad Complutense de Madrid

A metabelian group G acting as automorphism group on a compact Riemann surface of genus g ≥ 2 has order less than or equal to 16(g-1). We calculate for which values of g this bound is achieved and on these cases we calculate a presentation of the group G.

Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants

Alex Eskin, Howard Masur, Anton Zorich (2003)

Publications Mathématiques de l'IHÉS

A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description of...

Morphisms of Klein surfaces.

F. J. Cirre (1997)

Revista Matemática de la Universidad Complutense de Madrid

We give an elementary proof of a theorem of Andreian Cazacu on the behavior of morphisms of Klein surfaces under composition.

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