Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 439-455

CONVERGENCE OF SOME HOROCYCLIC DEFORMATIONS TO THE GARDINER-MASUR BOUNDARY

Vincent Alberge

Université de Strasbourg et CNRS, Institut de Recherche Mathématique Avancée
7 rue René Descartes, 67084 Strasbourg Cedex, France; alberge 'at' math.unistra.fr

Abstract. 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 Teichmüller space. This deformation, which we call the horocyclic deformation, is directed by a projective measured foliation and belongs to a certain horocycle in a Teichmüller disc. Using works of Marden and Masur in [12] and Miyachi in [16,17,20], we show that the horocyclic deformation converges if its direction is given by a simple closed curve or a uniquely ergodic measured foliation.

2010 Mathematics Subject Classification: Primary 30F60, 32G15, 30F45, 32F45.

Key words: Extremal length, Teichmüller space, Teichmüller distance, Thurston asymmetric metric, Teichmüller disc, Gardiner-Masur boundary, Thurston boundary.

Reference to this article: V. Alberge: Convergence of some horocyclic deformations to the Gardiner-Masur boundary. Ann. Acad. Sci. Fenn. Math. 41 (2016), 439-455.

Full document as PDF file

doi:10.5186/aasfm.2016.4132