Weil–Petersson class non-overlapping mappings into a Riemann surface

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2016-08

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en

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21

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Communications in Contemporary Mathematics, Volume 18, issue 04

Abstract

For a compact Riemann surface of genus g with n punctures, consider the class of n-tuples of conformal mappings (φ1, . . . , φn) of the unit disk each taking 0 to a puncture. Assume further that (1) these maps are quasiconformally extendible to C , (2) the pre-Schwarzian of each φi is in the Bergman space, and (3) the images of the closures of the disk do not intersect. We show that the class of such non-overlapping mappings is a complex Hilbert manifold.

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Radnell, D, Schippers, E & Staubach, W 2016, ' Weil–Petersson class non-overlapping mappings into a Riemann surface ', Communications in Contemporary Mathematics, vol. 18, no. 04, 1550060 . https://doi.org/10.1142/S0219199715500601