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

David Radnell; Eric Schippers; Wolfgang Staubach

doi:10.1142/S0219199715500601

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

David Radnell, Eric Schippers, Wolfgang Staubach

Department of Mathematics and Systems Analysis

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Abstract

For a compact Riemann surface of genus g with n punctures, consider the class of n-tuples of conformal mappings (φ₁, . . . , φ_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 φ_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.

Original language	English
Article number	1550060
Number of pages	21
Journal	Communications in Contemporary Mathematics
Volume	18
Issue number	04
DOIs	https://doi.org/10.1142/S0219199715500601
Publication status	Published - Aug 2016
MoE publication type	A1 Journal article-refereed

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

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