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Conformal Geometry and Dynamics

ISSN 1088-4173



The Teichmüller distance on the space of flat conformal structures

Author: Hiroyasu Izeki
Journal: Conform. Geom. Dyn. 2 (1998), 1-24
MSC (1991): Primary 58D27
Published electronically: February 3, 1998
MathSciNet review: 1600252
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Abstract: We define the Teichmüller pseudodistance on spaces of flat conformal structures by the same manner as classical Teichmüller distance on the Teichmüller space of Riemann surfaces. We will prove that for compact manifolds this pseudodistance becomes a complete distance. We will also prove similar results for noncompact manifolds under certain assumptions.

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Hiroyasu Izeki
Affiliation: Mathematical Institute, Tohoku University, Aoba-ku, Sendai, 980-77, Japan

Keywords: Conformally flat manifolds, quasiconformal mappings
Received by editor(s): February 24, 1997
Received by editor(s) in revised form: October 24, 1997
Published electronically: February 3, 1998
Article copyright: © Copyright 1998 American Mathematical Society