An interpolation theorem for proper holomorphic embeddings

Abstract

Given a Stein manifold x of dimension n > 1, a discrete sequence \(\{a_j\}\subset X\), and a discrete sequence \(\{b_j\}\subset \mathbb{C}^{m}\) where \(m\ge N=\left[\frac{3n}{2}\right] + 1\), there exists a proper holomorphic embedding \(f\colon X\hookrightarrow \mathbb{C}^{m}\) satisfying f(a j ) = b j for every j = 1,2,...