A complex structure on the set of quasiconformally extendible non-overlapping mappings into a Riemann surface
Abstract
Let be a compact Riemann surface with n distinguished points p1,...,pn. We prove that the set of n-tuples (φ1,...,φn) of univalent mappings φi from the open unit disc into mapping 0 to pi, 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.
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