Extendability of proper holomorphic mappings and global analytic hypoellipticity of the ∂̄-Neumann problem
Abstract
In this communication, the proof of the following theorem is sketched: If D 1 is a bounded domain in Cn with real analytic boundary whose ∂̄-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 Cn with real analytic boundary, then the mapping f extends to be holomorphic in a neighborhood of ¯D1. The proof relies on a transformation formula for the Bergman projection under proper holomorphic mappings.
