Holomorphic Approximation via Dolbeault Cohomology

2019/05/16 by Christine Laurent‐Thiébaut, Laurent-Thiébaut, Christine, Mei-Chi Shaw +1
Mathematics · #Advanced Banach Space Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1905.06556

openalex publication_date 2019/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study holomorphic approximation and approximation of ∂-closed forms in complex manifolds of complex dimension n≥ 1. We consider extensions of the classical Runge theorem and the Mergelyan property to domains in complex manifolds for the smooth and the L² 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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