1999/09/28 by M. Jarnicki, Jarnicki, M., P. Pflug +3
Mathematics · #32H10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32H10
paper · pdf · doi:10.48550/arxiv.math/9909164
13 pages
arxiv created 1999/09/28 · arxiv updated 2009/11/30
We study the problem of the boundary behaviour of the Bergman kernel and the Bergman completeness in some classes of bounded pseudoconvex domains, which contain also non-hyperconvex domains. Among the classes for which we prove the Bergman completeness and the convergence of the Bergman kernel to infinity while tending to the boundary are all bounded pseudoconvex balanced domains, all bounded Hartogs domains with balanced fibers over regular domains and some bounded Laurent-Hartogs domains.