Geometriae Dedicata

, Volume 137, Issue 1, pp 113–141

Teichmüller rays and the Gardiner–Masur boundary of Teichmüller space

Original Paper

DOI: 10.1007/s10711-008-9289-2

Cite this article as:
Miyachi, H. Geom Dedicata (2008) 137: 113. doi:10.1007/s10711-008-9289-2

Abstract

The aim of this paper is to develop the theory of a compactification of Teichmüller space given by F. Gardiner and H. Masur, which we call the Gardiner–Masur compactification of the Teichmüller space. We first develop the general theory of the Gardiner–Masur compactification. Secondly, we will investigate the asymptotic behaviors of Teichmüller geodesic rays under the Gardiner–Masur embedding. In particular, we will observe that the projective class of a rational measured foliation G can not be an accumulation point of every Teichmüller geodesic ray under the Gardiner–Masur embedding, when the support of G consists of at least two simple closed curves.

Keywords

Extremal length Teichmüller space Geodesic Gardiner–Masur boundary Thurston boundary 

Mathematics Subject Classification (2000)

30F60 32G15 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonaka, OsakaJapan

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