A complex structure on the set of quasiconformally extendible non-overlapping mappings into a Riemann surface
| Autor: | Eric Schippers, David Radnell |
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| Rok vydání: | 2009 |
| Předmět: |
Teichmüller space
Pure mathematics Mathematics - Complex Variables Mathematics::Complex Variables Conformal field theory General Mathematics Riemann surface Mathematical analysis Neighbourhood (graph theory) Universal Teichmüller space FOS: Physical sciences Mathematical Physics (math-ph) Banach manifold symbols.namesake Product (mathematics) FOS: Mathematics symbols Complex Variables (math.CV) Unit (ring theory) Mathematical Physics 30C55 30C62 30F60 (Primary) 81T40 (Secondary) Analysis Mathematics |
| Zdroj: | Journal d'Analyse Mathématique. 108:277-291 |
| ISSN: | 1565-8538 0021-7670 |
| DOI: | 10.1007/s11854-009-0025-0 |
| Popis: | Let \Sigma be a compact Riemann surface with n distinguished points p_1,...,p_n. We prove that the set of n-tuples (\phi_1,...,\phi_n) of univalent mappings \phi_i from the open unit disc into \Sigma mapping 0 to p_i, with non-overlapping images and quasiconformal extensions to a neighbourhood of the closed unit disk, carries a natural complex Banach manifold structure. This complex structure is locally modelled on the n-fold product of a two complex-dimensional extension of the universal Teichmueller space. Our results are motivated by Teichmueller theory and two-dimensional conformal field theory. Comment: 12 pages. Minor corrections made. To appear in Journal d'Analyse Mathematique |
| Databáze: | OpenAIRE |
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