Abstract
In this article we prove that if D ⊂ ℂ n , n ≥ 2, is a bounded pseudoconvex domain with real analytic boundary, then for each g(z) ∈ Aut(D), there exists a fixed open neighborhood Ω g of D̄ and an open neighborhood V g of g(z) in Aut(D) such that any h(z) ∈ V g can be extended holomorphically to Ω g , and that the action defined by π :V g × Ω g → ℂ n (f,z) → π(f,z) = f(z) is real analytic in joint variables. This extends H. Cartan's theorem beyond the boundary. Some applications are also discussed here. ©1999 American Mathematical Society.