Abstract

Let {Ωt:−1<t<1} be a family of bounded pseudoconvex domains and φt∈PSH(Ωt). Let Kt(z,w) denote the Bergman kernel with weight φt on Ωt. We study the continuity and Hölder continuity of Kt(z,w) in t. Several applications to singularity theory of psh functions are given, including a new proof of the openness theorem.

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