English

Proper holomorphic maps from the unit disk to some unit ball

Complex Variables 2016-08-10 v1

Abstract

We study proper rational maps from the unit disk to balls in higher dimensions. After gathering some known results, we study the moduli space of unitary equivalence classes of polynomial proper maps from the disk to a ball, and we establish a normal form for these equivalence classes. We also prove that all rational proper maps from the disk to a ball are homotopic in target dimension at least 22.

Keywords

Cite

@article{arxiv.1608.02885,
  title  = {Proper holomorphic maps from the unit disk to some unit ball},
  author = {John P. D'Angelo and Zhenghui Huo and Ming Xiao},
  journal= {arXiv preprint arXiv:1608.02885},
  year   = {2016}
}

Comments

12 pages; to appear in Proceedings AMS

R2 v1 2026-06-22T15:16:06.661Z