Mathematical Research Letters

Volume 15, Issue 4, July 2008 pp. 821-826.

Proper holomorphic disks in the complement of varieties in $\mathbb{C}^2$

Authors: Stefan Borell (1), Frank Kutzschebauch (2), and Erlend Fornaess Wold (3)
Author institution: Universität Bern (1), Universität Bern (2), and Universität Bern (3)

Summary: We prove that for any complete pluripolar set $X\subset\C^2$ (in particular for any analytic subset) there exists a proper holomorphic embedding $\phi\colon\triangle\emb\C^2$ of the open unit disk $\triangle\subset\C$ such that $\phi(\triangle)\cap X=\emptyset$. It follows that the same holds true in $\C^n$ for any $n>1$.

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