Holomorphic Approximation via Dolbeault Cohomology

Christine Laurent-Thiébaut; Mei-Chi Shaw

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arXiv · 1905.06556

Holomorphic Approximation via Dolbeault Cohomology

Christine Laurent-Thiébaut·Mei-Chi Shaw

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Abstract

The purpose of this paper is to study holomorphic approximation and approximation of $\bar\partial$-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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Christine Laurent-Thiébaut, Mei-Chi Shaw. 2019-05-16. Holomorphic Approximation via Dolbeault Cohomology. https://arxiv.org/abs/1905.06556

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