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

David Radnell; Eric Schippers; Wolfgang Staubach

doi:10.1090/ecgd/332

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

David Radnell^*
, Eric Schippers
, Wolfgang Staubach

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

7 Citations (Scopus)

199 Downloads (Pure)

Abstract

We consider Riemann surfaces S with Σ borders homeomorphic to 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.

Original language	English
Pages (from-to)	32-51
Number of pages	20
Journal	Conformal Geometry and Dynamics
Volume	23
Issue number	3
DOIs	https://doi.org/10.1090/ecgd/332
Publication status	Published - 27 Feb 2019
MoE publication type	A1 Journal article-refereed

Funding

The first author acknowledges the support of the Academy of Finland's project "Algebraic structures and random geometry of stochastic lattice models".

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10.1090/ecgd/332

A_Model_of_the_Teichmuller_space_of_genus_zero_bordered_surfaces_by_period_mapsAccepted author manuscript, 424 KB

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AB - We consider Riemann surfaces S with Σ borders homeomorphic to 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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A Model of the Teichmüller space of genus-zero bordered surfaces by period maps

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