107 research outputs found
Serre Duality on Domains in Complex Manifolds and Applications
An version of the Serre duality on domains in complex manifolds
involving duality of Hilbert space realizations of the
-operator is established. This duality is used to study the
solution of the -equation with prescribed support. Applications
are given to -closed extension of forms, as well to
Bochner-Hartogs type extension of CR functions.Comment: Typos corrected and new references added. To appear in the
Transactions of the AM
Holomorphic Approximation via Dolbeault Cohomology
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
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