A Complex Structure on the Set of Quasiconformally Extendible Non-overlapping Mappings into a Riemann Surface
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چکیده
Let Σ 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 unit disc D into Σ mapping 0 to pi, with non-overlapping images and quasiconformal extensions to a neighbourhood of D, 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 Teichmüller space. Our results are motivated by Teichmüller theory and two-dimensional conformal field theory.
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تاریخ انتشار 2008