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Weil-Petersson class non-overlapping mappings into a Riemann surface
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.
2016 (English)In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 18, no 4, 1550060Article in journal (Refereed) Published
Abstract [en]

For a compact Riemann surface of genus g with n punctures, consider the class of n-tuples of conformal mappings (phi(1),..., phi(n)) 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 phi(i) 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.

Place, publisher, year, edition, pages
2016. Vol. 18, no 4, 1550060
Keyword [en]
L-2 Beltrami differentials, Teichmuller theory
National Category
URN: urn:nbn:se:uu:diva-303743DOI: 10.1142/S0219199715500601ISI: 000381203200007OAI: oai:DiVA.org:uu-303743DiVA: diva2:973879
Available from: 2016-09-23 Created: 2016-09-23 Last updated: 2016-09-28

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Radnell, DavidStaubach, Wolfgang
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