Proper holomorphic disks in the complement of varieties in \C^2

TL;DR

This paper proves that for any closed analytic set in c2, there exists a proper holomorphic embedding of the unit disk into c2 avoiding that set, demonstrating a significant flexibility in complex analysis.

Contribution

It establishes the existence of proper holomorphic disks in the complement of any closed analytic set in c2, extending previous results on holomorphic embeddings.

Findings

Existence of proper holomorphic embeddings avoiding any closed analytic set in c2.

Construction methods for such embeddings.

Implications for complex geometry and function theory.

Abstract

For any closed analytic set X in C^2 there exists a proper holomorphic embedding of the unit disk into C^2 such that the image avoids X.