# HOLOMORPHIC APPROXIMATION VIA DOLBEAULT COHOMOLOGY

Abstract : The 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.
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Journal articles

Cited literature [14 references]

https://hal.archives-ouvertes.fr/hal-02130114
Contributor : Christine Laurent-Thiébaut <>
Submitted on : Wednesday, January 8, 2020 - 3:28:15 PM
Last modification on : Tuesday, November 24, 2020 - 4:00:16 PM

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### Identifiers

• HAL Id : hal-02130114, version 2
• ARXIV : 1905.06556

### Citation

Christine Laurent-Thiébaut, Mei-Chi Shaw. HOLOMORPHIC APPROXIMATION VIA DOLBEAULT COHOMOLOGY. Mathematische Zeitschrift, Springer, In press. ⟨hal-02130114v2⟩

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