Variations of Abelian differentials under quasiconformal deformations
type: Item
instance of: scholarly article
title: Variations of Abelian differentials under quasiconformal deformations
zbMATH Open document ID: 0536.32007
DOI: 10.1007/BF01182383
author: Yukio Kusunoki
author: Fumio Maitani
published in: Mathematische Zeitschrift
publication date: 1982-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173245
review text: The well-known result of \textit{L. V. Ahlfors} and \textit{L. Bers} in ''Analytic functions'', Princeton Math. Ser. 24, 45-66 and 89-119 (1960; the both Zbl 0100.289) and of \textit{L. Bers} in Bull. Lond. Math. Soc. 4, 257-300 (1972; Zbl 0257.32012) on Riemann's period matrices and Abelian differentials of a Riemann surface of finite type has recently been extended to the case of a certain class O'' of open Riemann surfaces [the first author, Hokkaido Math. J. 10, Special issue, 435-446 (1981; Zbl 0485.32011)]. Following these methods the authors attempt to discuss the above property and related ones for the case of arbitrary open Riemann surfaces [see also the first author and \textit{M. Taniguchi}, Ann. Acad. Sci. Fenn., Ser. A I 5, 207-226 (1980; Zbl 0458.30028)].
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 30F30
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 3851496
zbMATH Keywords: open Riemann surfaces
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Abelian differentials
zbMATH Keywords: period matrices
zbMATH Keywords: normal behavior
zbMATH Keywords: quasiconformal deformations
reviewed by: Boris N. Apanasov
MaRDI profile type: Publication
cites work: Q3282112
cites work: Q5512337
cites work: Q5593095
cites work: Holomorphic differentials as functions of moduli
cites work: Q5516254
cites work: Differentiability of period matrices in Teichmüller spaces
cites work: A continuity property of holomorphic differentials under quasiconformal deformations
cites work: The method of linear operators for square integrable differentials on open Riemann surfaces and its applications
cites work: Q5547021
cites work: Square Integrable Differentials on Riemann Surfaces and Quasiconformal Mappings
OpenAlex ID: W2002844538
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description: scientific article; zbMATH DE number 3851496