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On the Bergman kernel and biholomorphic mappings of pseudoconvex domains

1974
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Bulletin of the American Mathematical Society
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Communicated by E. M. Stein, October 30, 1973 THEOREM 1. Let D x , D 2^C n be strictly pseudoconvex domains with smooth boundaries and suppose that F\D 1 -^D 2 is biholomorphic (i.e., F is an analytic homeomorphism). Then F extends to a diffeomorphism of the closures, F: D 1 ->D 2 . The main idea in proving Theorem 1 is to study the boundary behavior of geodesies in the Bergman metrics (see [2] ) of Z>i and D 2 . To do so, we use a rather explicit formula for the Bergman kernels of D x and D 2

doi:10.1090/s0002-9904-1974-13539-1
fatcat:qgjdrejz5jchfnfjbpma57qa4u