Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2017-06-29
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en
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17
229-245
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JOURNAL D ANALYSE MATHEMATIQUE, Volume 132, issue 1
Abstract
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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Radnell , D , Schippers , E & Staubach , W 2017 , ' Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials ' , JOURNAL D ANALYSE MATHEMATIQUE , vol. 132 , no. 1 , pp. 229-245 . https://doi.org/10.1007/s11854-017-0020-9