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

David Radnell, Eric Schippers

Let 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 Σm…