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Geometriae Dedicata

, Volume 162, Issue 1, pp 283–304 | Cite as

Teichmüller rays and the Gardiner–Masur boundary of Teichmüller space II

  • Hideki Miyachi
Original Paper

Abstract

In this paper, we study the asymptotic behavior of Teichmüller geodesic rays in the Gardiner–Masur compactification. We will observe that any Teichmüller geodesic ray converges in the Gardiner–Masur compactification. Therefore, we get a mapping from the space of projective measured foliations to the Gardiner–Masur boundary by assigning the limits of associated Teichmüller rays. We will show that this mapping is injective but is neither surjective nor continuous. We also discuss the set of points where this mapping is bicontinuous.

Keywords

Teichmüller space Teichmüller geodesic rays Gardiner–Masur boundary Thurston boundary 

Mathematics Subject Classification

30F60 32G15 32F45 57M50 

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

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

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