Erschienen in:

1984 | OriginalPaper | Buchkapitel

RIEMANN Extension Theorem and Analytic Coverings

verfasst von : Hans Grauert, Reinhold Remmert

Erschienen in: Coherent Analytic Sheaves

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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If p is a point in a domain D ⊂ ℂ, then each bounded holomorphic function f in D\p has a unique holomorphic extension to D. The same is true for domains D in ℂn,1 ≤ n < ∞, if p is replaced by a nowhere dense analytic set A in D. If A has dimension ≤n −2 everywhere it is no longer necessary to assume that f is bounded in D\A. These two statements are known as the Riemann Extension Theorems; for the convenience of the reader we reproduce proofs in Section 1.

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