English

Holomorphic isometries between products of complex unit balls

Complex Variables 2017-06-26 v1

Abstract

We first give an exposition on holomorphic isometries from the Poincar\'e disk to polydisks and from the Poincar\'e disk to the product of the Poincar\'e disk with a complex unit ball. As an application, we provide an example of proper holomorphic map from the unit disk to the complex unit ball that is irrational, algebraic and holomorphic on a neighborhood of the closed unit disk. We also include some new results on holomorphic isometries.

Keywords

Cite

@article{arxiv.1706.07782,
  title  = {Holomorphic isometries between products of complex unit balls},
  author = {Shan Tai Chan and Ming Xiao and Yuan Yuan},
  journal= {arXiv preprint arXiv:1706.07782},
  year   = {2017}
}
R2 v1 2026-06-22T20:27:57.413Z