Mathematical Research Letters

Volume 15 (2008)

Number 4

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

Pages: 821 – 826



Stefan Borell (Universität Bern)

Frank Kutzschebauch (Universität Bern)

Erlend Fornaess Wold (Universität Bern)


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 $n >1$.

Published 1 January 2008