Extendability of proper holomorphic mappings and global analytic hypoellipticity of the partial differential-Neumann problem.
IN THIS COMMUNICATION, THE PROOF OF THE FOLLOWING THEOREM IS SKETCHED: If D(1) is a bounded domain in C(n) with real analytic boundary whose partial differential-Neumann problem is globally real analytic hypoelliptic and f is a proper holomorphic mapping of D(1) onto a second bounded domain D(2) in C(n) with real analytic boundary, then the mapping f extends to be holomorphic in a neighborhood of D(1). The proof relies on a transformation formula for the Bergman projection under proper holomorphic mappings.
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Mathematics Department, Princeton University, Princeton, New Jersey 08544.