The Teichmüller space of a countable set of points on a Riemann surface

Fujikawa, Ege; Taniguchi, Masahiko

doi:10.1090/ecgd/301

The Teichmüller space of a countable set of points on a Riemann surface
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by Ege Fujikawa and Masahiko Taniguchi PDF

Conform. Geom. Dyn. 21 (2017), 64-77 Request permission

Abstract:

We introduce the quasiconformal deformation space of an ordered countable set of an infinite number of points on a Riemann surface and give certain conditions under which it admits a complex structure via Teichmüller spaces of associated subsurfaces with the complement of the set of points. In a similar fashion, we give another definition of the quasiconformal deformation space of a finitely generated Kleinian group.

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