Einbettungen Steinscher Mannigfaltigkeiten

Abstract

A well-known conjecture in geometric function theory is the conjecture of Forster, namely that there exists an embedding of a Stein manifold of dimension n in an affine space$\mathbb{C}^{n + 1 + [\tfrac{n}{2}]}$. A first step to prove this was a theorem of Forster, which gives an embedding of a Stein manifold of dimension n into$\mathbb{C}^{2n - [{{(n - 2)} \mathord{\left/ {\vphantom {{(n - 2)} 3}} \right. \kern-\nulldelimiterspace} 3}]}$ for n—6. The goal of this paper is an amelioration of Forster's result. It follows the main lines of Forster's proof. It is proved that the conjecture holds “asymptotically”.