## HOLOMORPHIC APPROXIMATION VIA DOLBEAULT COHOMOLOGY

### 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]