Variation of Bergman kernels of pseudoconvex domains

Abstract

We shall give a variational formula of the full Bergman kernels associated to a family of smoothly bounded strongly pseudoconvex domains. An equivalent criterion for the triviality of holomorphic motions of planar domains in terms of the Bergman kernel is given as an application.

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• Curvatures of direct image sheaves of vector bundles and applications I
• Variation of the Bergman kernels under deformations of complex structures