Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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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