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Random walks in ( ℤ + ) 2 with non-zero drift absorbed at the axes

Irina Kurkova, Kilian Raschel (2011)

Bulletin de la Société Mathématique de France

Spatially homogeneous random walks in ( ℤ + ) 2 with non-zero jump probabilities at distance at most 1 , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.

Real Schottky uniformizations and Jacobians of May surfaces.

Rubén A. Hidalgo, Rubí E. Rodríguez (2004)

Revista Matemática Iberoamericana

Given a closed Riemann surface R of genus p ≥ 2 together with an anticonformal involution τ : R ---> R with fixed points, we consider the group K(R, τ) consisting of the conformal and anticonformal automorphisms of R which commute with τ...

Reduced Bers boundaries of Teichmüller spaces

Ken’ichi Ohshika (2014)

Annales de l’institut Fourier

We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space lying there into a point.This boundary turns out to be independent of the basepoint, and the action of the mapping class group extends continuously to this boundary.This is an affirmative answer to Thurston’s conjecture.He also conjectured that this boundary is homeomorphic to the unmeasured lamination space by the correspondence coming...

Regular and limit sets for holomorphic correspondences

S. Bullett, C. Penrose (2001)

Fundamenta Mathematicae

Holomorphic correspondences are multivalued maps f = Q ̃ ₊ Q ̃ ₋ - 1 : Z → W between Riemann surfaces Z and W, where Q̃₋ and Q̃₊ are (single-valued) holomorphic maps from another Riemann surface X onto Z and W respectively. When Z = W one can iterate f forwards, backwards or globally (allowing arbitrarily many changes of direction from forwards to backwards and vice versa). Iterated holomorphic correspondences on the Riemann sphere display many of the features of the dynamics of Kleinian groups and rational maps, of which...

Riemann and Klein surfaces with nodes viewed as quotients.

Ignacio C. Garijo (2006)

Revista Matemática Complutense

If G is a group of automorphisms that acts properly discontinuously on a Riemann or Klein surface X, then there exists a unique structure of Riemann or Klein surface on X/G such that the projection π: X → X/G is a morphism. The analogous result is not true when we deal with surfaces with nodes. In this paper we give a new definition of a group that acts properly discontinuously on a surface with nodes in order to obtain a similar theorem.

Riemann surfaces with boundary and natural triangulations of the Teichmüller space

Gabriele Mondello (2011)

Journal of the European Mathematical Society

We compare some natural triangulations of the Teichmüller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell–Wolf’s proof to show that grafting semi-infinite cylinders at the ends of hyperbolic surfaces with fixed boundary lengths is a homeomorphism. This way, we construct a family of equivariant triangulations of the Teichmüller space of punctured surfaces that interpolates between Bowditch–Epstein–Penner’s (using the spine construction) and Harer–Mumford–Thurston’s...

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