Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 947-971

INTRODUCTION OF A COMPLEX STRUCTURE ON THE p-INTEGRABLE TEICHMÜLLER SPACE

Masahiro Yanagishita

Waseda University, Departments in Fundamental Science and Engineering
3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan; m-yanagishita 'at' asagi.waseda.jp

Abstract. For p ≥ 1, the p-integrable Teichmüller space is the metric subspace of the Teichmüller space composed of the Teichmüller equivalence classes with p-integrable Beltrami coefficient. In this paper, for p ≥ 2, we introduce a complex structure on the p-integrable Teichmüller space of an arbitrary Fuchsian group satisfying a certain geometric condition. As an application, we show the coincidence of two canonical distances on the metric subspace.

2010 Mathematics Subject Classification: Primary 30F60; Secondary 32G15, 30C60.

Key words: Teichmüller spaces, quasiconformal mappings, Douady-Earle extension.

Reference to this article: M. Yanagishita: Introduction of a complex structure on the p-integrable Teichmüller space. Ann. Acad. Sci. Fenn. Math. 39 (2014), 947-971.

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doi:10.5186/aasfm.2014.3952