2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165077Let Σbe a compact Riemann surface with n distinguished points p_1,...,p_n. We prove that the set of n-tuples (ϕ_1,...,ϕ_n) of univalent mappings ϕ_i from the open unit disc into Σmapping 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.12 pages. Minor corrections made. To appear in Journal d'Analyse MathematiqueComplex VariablesMathematical Physics30C55, 30C62, 30F60 (Primary) 81T40 (Secondary)text