HOLOMORPHIC APPROXIMATION VIA DOLBEAULT COHOMOLOGY

Christine Laurent-Thiébaut (1) , Mei-Chi Shaw (2)

1 IF - Institut Fourier
2 UND - University of Notre Dame [Indiana]

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.

Mots clés: Runge's theorem; and phrases Runge's theorem; Mergelyan property; Dolbeault cohomology

Domaines: Variables complexes [math.CV]

Christine Laurent-Thiébaut, Mei-Chi Shaw. HOLOMORPHIC APPROXIMATION VIA DOLBEAULT COHOMOLOGY. Mathematische Zeitschrift, 2020, 296 (3-4), pp.1027-1047. ⟨10.1007/s00209-020-02470-3⟩. ⟨hal-02130114v2⟩