A Model of the Teichmüller space of genus-zero bordered surfaces by period maps

Radnell, David; Schippers, Eric; Staubach, Wolfgang

doi:10.1090/ecgd/332

A Model of the Teichmüller space of genus-zero bordered surfaces by period maps
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by David Radnell, Eric Schippers and Wolfgang Staubach

Conform. Geom. Dyn. 23 (2019), 32-51

DOI: https://doi.org/10.1090/ecgd/332

Published electronically: February 27, 2019

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Abstract:

We consider Riemann surfaces $\Sigma$ with $n$ borders homeomorphic to $\mathbb {S}^1$ and no handles. Using generalized Grunsky operators, we define a period mapping from the infinite-dimensional Teichmüller space of surfaces of this type into the unit ball in the linear space of operators on an $n$-fold direct sum of Bergman spaces of the disk. We show that this period mapping is holomorphic and injective.

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