Weil-Petersson class non-overlapping mappings into a Riemann surface
2016 (English)In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 18, no 4, 1550060Article in journal (Refereed) Published
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
L-2 Beltrami differentials, Teichmuller theory
IdentifiersURN: urn:nbn:se:uu:diva-303743DOI: 10.1142/S0219199715500601ISI: 000381203200007OAI: oai:DiVA.org:uu-303743DiVA: diva2:973879