Holomorphic Approximation via Dolbeault Cohomology
Complex Variables
2020-01-14 v2
Abstract
The purpose of this paper is to study holomorphic approximation and approximation of -closed forms in complex manifolds of complex dimension . We consider extensions of the classical Runge theorem and the Mergelyan property to domains in complex manifolds for the smooth and the topology. We characterize the Runge or Mergelyan property in terms of certain Dolbeault cohomology groups and some geometric sufficient conditions are given.
Cite
@article{arxiv.1905.06556,
title = {Holomorphic Approximation via Dolbeault Cohomology},
author = {Christine Laurent-Thiébaut and Mei-Chi Shaw},
journal= {arXiv preprint arXiv:1905.06556},
year = {2020}
}