Schiffer variation of complex structure and coordinates for Teichmüller spaces
type: Item
instance of: scholarly article
title: Schiffer variation of complex structure and coordinates for Teichmüller spaces
zbMATH Open document ID: 0591.32025
DOI: 10.1007/BF02880990
author: Subhashis Nag
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
review text: This paper concerns the problem of constructing explicit variations of complex structure on a Riemann surface so that the variation parameters provide complex-analytic and real-analytic coordinates for Teichmüller space. It is shown that Schiffer variations at independent points give local coordinates for Teichmüller space. Moreover, it is shown how to generalize this idea to infinite dimensional Teichmüller spaces. The duality between the sequence spaces \(\ell '\) and \(\ell^{\infty}\) corresponds to the duality between integrable cusp forms and bounded cusp forms. Moreover, for a properly chosen countable family of Schiffer variations, a neighborhood of the origin in the sequence space \(\ell^{\infty}\) becomes a local chart for Teichmüller space.
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30C70
zbMATH DE Number: 3948729
zbMATH Keywords: quasiconformal mapping
zbMATH Keywords: variations of complex structure on a Riemann surface
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Schiffer variations
reviewed by: Frederick P. Gardiner
MaRDI profile type: Publication
cites work: Q5512337
cites work: Q3282112
cites work: Reduced Teichmuller Spaces
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cites work: Q5832232
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full work available at URL: https://doi.org/10.1007/bf02880990
OpenAlex ID: W2017768612
description: scientific article; zbMATH DE number 3948729