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HOLOMORPHIC APPROXIMATION VIA DOLBEAULT COHOMOLOGY

By Christine Laurent-Thiébaut and Mei-Chi Shaw

Abstract

International audienceThe purpose of this paper is to study holomorphic approximation and approximation of $\overline\partial$-closed forms in complex manifolds of complex dimension $n\geq 1$. We consider extensions of the classical Runge theorem and the Mergelyan property to domains in complex manifolds for the smooth and the $L^2$ topology. We characterize the Runge or Mergelyan property in terms of certain Dolbeault cohomology groups and some geometric sufficient conditions are given

Topics: and phrases Runge's theorem, Runge's theorem, Mergelyan property, Dolbeault cohomology, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
Publisher: 'Springer Fachmedien Wiesbaden GmbH'
Year: 2020
OAI identifier: oai:HAL:hal-02130114v2
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