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Conformal Geometry and Dynamics

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


Authors: David Radnell, Eric Schippers and Wolfgang Staubach
Journal: Conform. Geom. Dyn. 23 (2019), 32-51
MSC (2010): Primary 30F60, 32G15, 32G20; Secondary 30C55, 30H20, 46G20
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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Additional Information

David Radnell
Affiliation: Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
Email: david.radnell@aalto.fi

Eric Schippers
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
Email: eric.schippers@umanitoba.ca

Wolfgang Staubach
Affiliation: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden
Email: wulf@math.uu.se

DOI: https://doi.org/10.1090/ecgd/332
Received by editor(s): October 18, 2017
Published electronically: February 27, 2019
Additional Notes: The first author acknowledges the support of the Academy of Finland’s project “Algebraic structures and random geometry of stochastic lattice models”.
The second and third authors are grateful for the financial support from the Wenner-Gren Foundations. The second author was also partially supported by the National Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 2019 American Mathematical Society