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}
}