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arXiv · 1703.08594

Proper holomorphic immersions into Stein manifolds with the density property

Franc Forstneric
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Abstract

In this paper we prove that every Stein manifold $S$ admits a proper holomorphic immersion into any Stein manifold $X$ of dimension $2\mathrm{dim}S$ enjoying the density property or the volume density property. The case $\mathrm{dim}S=1$ 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 $n=2\mathrm{dim}S$, and it complements the proper embedding theorem proved by Andrist et al. when $\mathrm{dim}X>2\mathrm{dim}S$ (J. Anal. Math., 130:135-150, 2016).

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Franc Forstneric. 2018-10-01. Proper holomorphic immersions into Stein manifolds with the density property. https://doi.org/10.1007/s11854-019-0068-9

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