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

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Research units

  • University of Manitoba
  • Uppsala University


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.


Original languageEnglish
Article number1550060
Number of pages21
JournalCommunications in Contemporary Mathematics
Issue number04
Publication statusPublished - Aug 2016
MoE publication typeA1 Journal article-refereed

ID: 6931037