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Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials
Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 132, no 1, p. 229-245Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. Vol. 132, no 1, p. 229-245
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-285998DOI: 10.1007/s11854-017-0020-9ISI: 000404532200009OAI: oai:DiVA.org:uu-285998DiVA, id: diva2:921413
Available from: 2016-04-20 Created: 2016-04-20 Last updated: 2017-10-03Bibliographically approved

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Staubach, Wolfgang

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