Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials
2015 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538Article in journal (Refereed) Accepted
Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1 . Consider quasiconformal maps f : Σ → Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t,·) : Σ → Σ1 is independent of t on the boundary curves; that is H(t,p) = f(p) for all p ∈ ∂Σ.
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IdentifiersURN: urn:nbn:se:uu:diva-285998OAI: oai:DiVA.org:uu-285998DiVA: diva2:921413