A complex structure on the set of quasiconformally extendible non-overlapping mappings into a Riemann surface

David Radnell*, Eric Schippers

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

Let Σ be a Riemann surface with n distinguished points p1,..., pn. We prove that the set of n-tuples (Φ1,..., Φn) of univalent mappings Φi from the unit disc D into Σ mapping 0 to pi, with non-overlapping images and quasiconformal extensions to a neighbourhood of D̄, carries a natural complex Banach manifold structure. This complex structure is locally modeled on the n-fold product of a two complex-dimensional extension of the universal Teichmüller space. Our results are motivated by Teichmüller theory and two-dimensional conformal field theory.

Original languageEnglish
Pages (from-to)277-291
Number of pages15
JournalJournal d'Analyse Mathematique
Volume108
Issue number1
DOIs
Publication statusPublished - Sep 2009
MoE publication typeA1 Journal article-refereed

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