Abelian Teichmüller disks restricted by behavior

2009-04-07T07:01:48Z

2009-04-07T07:01:48Z

1987-03

We shall investigate quasiconformal deformations of arbitrary Riemann surfaces whose Riemannian metrics are given by Beltrami differentials with complex parameters in the unit disk, where the Beltrami differentials are represented by certain holomorphic differentials with restricted boundary behavior. They are so called Abelian Teichmüller disks. For the sake of discussion on general open Riemann surfaces, we consider two types of boundary behavior. The one is based on Dirichlet finite harmonic differentials with integral periods and the other is based on holomorphic differentials with normal behavior. By using the arguments of F.Gardiner and I.Kra on punctured Riemann surfaces, we shall discuss extremal quasiconformal mappings in Torelli space, variational formulas of the norms of our restricted holomorphic differentials and Torelli's theorem on our Abelian Teichmüller disks of an arbitrary Riemann surface.

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Reprinted from the Memoirs of the Faculty of Engineering and Design, Kyoto Institute of Technology, Series of Science and Technology, Vol.35 (1986) pp.1-11

http://hdl.handle.net/10212/1906

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