Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.28089

Authors: Du, Yun-Heng, Guo, Bin, Wang, Peng-Chao, Xie, Song-Yan

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214237809

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