The extension of regular holomorphic maps

Abstract

Let f f be a holomorphic map of a k k -dimensional polydisk in C n {C^n} into an n n -dimensional complex manifold M M which is regular at the origin. It is shown that f f can be extended to a neighborhood in C n {C^n} of a slightly smaller polydisk so that the extension is also regular. If f f is an embedding or immersion, then the extension may also be taken to be an embedding or immersion.