Boundary values of pluriharmonic functions with Bott-Chern cohomology

Abstract

The main purpose of this paper is to investigate the relationship between continuation of pluriharmonic functions from the boundary of an unbounded domain and the vanishing of the Bott-Chern cohomology with supports in a paracompactifying family of closed subset of a complex manifold X. We moreover give a relation between distributional boundary values and extensible currents.