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arXiv · 1710.06960

A Model of the Teichm\"uller space of genus-zero bordered surfaces by period maps

David Radnell·Eric Schippers·Wolfgang Staubach
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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 Teichm\"uller 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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David Radnell, Eric Schippers, Wolfgang Staubach. 2017-10-18. A Model of the Teichm\"uller space of genus-zero bordered surfaces by period maps. https://arxiv.org/abs/1710.06960

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