The Teichmüller distance on the space of flat conformal structures

Izeki, Hiroyasu

doi:10.1090/S1088-4173-98-00009-5

The Teichmüller distance on the space of flat conformal structures
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by Hiroyasu Izeki

Conform. Geom. Dyn. 2 (1998), 1-24

DOI: https://doi.org/10.1090/S1088-4173-98-00009-5

Published electronically: February 3, 1998

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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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