Proper holomorphic immersions into Stein manifolds with the density property

Abstract

In this paper we prove that every Stein manifold $S$ admits a proper holomorphic immersion into any Stein manifold $X$ of dimension $2\dim S$ enjoying the density property or the volume density property. The case $\dim S=1$ was proved beforehand by Andrist and Wold (Ann. Inst. Fourier (Grenoble), 64(2):681-697, 2014). This result generalizes the classical theorem of Bishop and Narasimhan for immersions to ${\mathbb{C}}^n$ with $n=2\dim S$, and it complements the proper embedding theorem proved by Andrist et al. when $\dim X>2\dim S$ (J. Anal. Math., 130:135-150, 2016).

J. Anal. Math., to appear. Remark 1.3 has been added in this version

References in corpus (2)

• Criteria for the density property of complex manifolds
• Riemann surfaces in Stein manifolds with density property

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