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- W4256243463 abstract "In analogy with the Hartogs theorem that separate analyticity of a function implies analyticity, it is shown that a separately normal family of holomorphic maps from a polydisk into a Riemann surface is a normal family. This contrasts with examples of discontinuous separately analytic maps from a bidisk into the Riemann sphere. The proof uses a theorem on pseudoconvexity of normality domains, which is proved via the following convergence criterion: a sequence ${ {f_j}}$ of holomorphic maps from a complex manifold into a Riemann surface converges to a nonconstant holomorphic map if and only if the sequence ${ f_j^{ - 1}}$ of set-valued maps, defined on the Riemann surface, converges to a suitable set-valued map. Extending Osgoodâs theorem, it is also shown that a separately analytic map (resp. a separately normal family of holomorphic maps) from a polydisk into a hyperbolic complex space is analytic (resp. normal)." @default.
- W4256243463 created "2022-05-12" @default.
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- W4256243463 date "1975-06-01" @default.
- W4256243463 modified "2023-10-14" @default.
- W4256243463 title "Families of Holomorphic Maps into Riemann Surfaces" @default.
- W4256243463 doi "https://doi.org/10.2307/1997173" @default.
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