Periodic transport and Oka complements in \(\C^n\)

Abstract

For every \(n\geq2\), we prove that the complement in \(\C^n\) of a periodic closed set with compact holomorphically convex quotient in \((\C^*)^n\) is Oka. The proof combines periodic divergence-free transport with Fatou--Bieberbach basins. Applications include complements of convex tubes \(\R^n+\ii B\), products of closed annuli, and, more generally, products of planar compact sets whose complements have at most one bounded component. In particular, \(\C^2\setminus\R^2\) is Oka.