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For p ≥ 1, the p-integrable Teichmuller space is the metric subspace of the Teich- muller space composed of the Teichmuller equivalence classes with p-integrable Beltrami coefficient. In this paper, for p ≥ 2, we introduce a complex structure on the p-integrable Teichmuller 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.

Introduction of a complex structure on the p-integrable Teichmüller space