Holomorphic approximation and holomorphic convexity on pseudoconvex complex manifolds *

Abstract

Let Ω be a complex submanifold with C 3 pseudoconvex boundary such that there is a function λεC 3 which is strongly plurisubharmonic in a neighborhood of the boundary of Ω. We prove the Oka-Weil approximation theorem on Ω. Also we show that Ω is holomorphically convex and that the plurisubharmonic hull and the holomorphic hull coincide for Ω. The methods of proof of the above results rely on the elementary -estimates introduced by Hörmander ([2], [3])