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

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

7 Sitaatiot (Scopus)

86 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Artikkeli	1550060
Sivumäärä	21
Julkaisu	Communications in Contemporary Mathematics
Vuosikerta	18
Numero	04
DOI - pysyväislinkit	https://doi.org/10.1142/S0219199715500601
Tila	Julkaistu - elok. 2016
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1142/S0219199715500601

Weil-Petersson class non-overlapping mappings RSS 2015Accepted author manuscript, 347 KB

Siteeraa tätä

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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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