Variations of Abelian differentials under quasiconformal deformations
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)].
scientific article; zbMATH DE number 3851496
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