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

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Weil–Petersson class non-overlapping mappings into a Riemann surface. / Radnell, David; Schippers, Eric; Staubach, Wolfgang.

In: Communications in Contemporary Mathematics, Vol. 18, No. 04, 1550060, 08.2016.

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@article{fb208f8a468b4d7197b644fdf356cbb1,
title = "Weil–Petersson class non-overlapping mappings into a Riemann surface",
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.",
author = "David Radnell and Eric Schippers and Wolfgang Staubach",
year = "2016",
month = "8",
doi = "10.1142/S0219199715500601",
language = "English",
volume = "18",
journal = "Communications in Contemporary Mathematics",
issn = "0219-1997",
publisher = "World Scientific Publishing Co.",
number = "04",

}

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TY - JOUR

T1 - Weil–Petersson class non-overlapping mappings into a Riemann surface

AU - Radnell, David

AU - Schippers, Eric

AU - Staubach, Wolfgang

PY - 2016/8

Y1 - 2016/8

N2 - 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.

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.

U2 - 10.1142/S0219199715500601

DO - 10.1142/S0219199715500601

M3 - Article

VL - 18

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - 04

M1 - 1550060

ER -

ID: 6931037