Bergman kernel and metric on non-smooth pseudoconvex domains

摘要

A stability theorem of the Bergman kernel and completeness of the Bergman metric have been proved on a type of non-smooth pseudoconvex domains defined in the following way: D={z∈U|r(z)0} where U is a neighbourhood of (?) and r is a continuous plurisubharmonic function on U. A continuity principle of the Bergman Kernel for pseudoconvex domains with Lipschitz boundary is also given, which answers a problem of Boas.