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PreprintarXiv licencearXiv

Periodic transport and Oka complements in Cn

  • Yun-Heng Du
  • Bin Guo
  • Peng-Chao Wang
  • Song-Yan Xie
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Abstract

For every n≥2, we prove that the complement in Cn 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 Rn+ii B, products of closed annuli, and, more generally, products of planar compact sets whose complements have at most one bounded component. In particular, C2∖R2 is Oka.

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Cite

BibTeXRIS
BibTeX
@misc{du2026periodic,
  title = {{Periodic transport and Oka complements in \(\C^n\)}},
  author = {Yun-Heng Du and Bin Guo and Peng-Chao Wang and Song-Yan Xie},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28089},
  eprint = {2609.28089},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28089},
}
RIS
TY  - UNPB
TI  - Periodic transport and Oka complements in C^n
AU  - Yun-Heng Du
AU  - Bin Guo
AU  - Peng-Chao Wang
AU  - Song-Yan Xie
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.28089
UR  - https://arxiv.org/abs/2609.28089
AB  - For every n≥2, 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∖R^2 is Oka.
ER  -