Convergence of some horocyclic deformations to the Gardiner-Masur boundary

Vincent Alberge (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We introduce a deformation of Riemann surfaces and we are interested in the convergence of this deformation to a point of the Gardiner-masur boundary of Teichmueller space. This deformation, which we call the horocyclic deformation, is directed by a projective measured foliation and belongs to a certain horocycle in a Teichmueller disc. Using works of Marden and Masur and works of Miyachi, we show that the horocyclic deformation converges if its direction is given by a simple closed curve or a uniquely ergodic measured foliation.

Mots clés: Extremal length; Teichmueller space; Teichmueller disc; Teichmueller metric; Thurston asymmetric metric; Gardiner-Masur boundary; Thurston boundary.

Domaines: Variables complexes [math.CV]; Topologie géométrique [math.GT]

Vincent Alberge. Convergence of some horocyclic deformations to the Gardiner-Masur boundary. Annales Academiae Scientiarum Fennicae. Mathematica, 2016, ⟨10.5186/aasfm.2016.4132⟩. ⟨hal-01167993⟩