Proper holomorphic maps between bounded symmetric domains revisited
type: Item
instance of: scholarly article
title: Proper holomorphic maps between bounded symmetric domains revisited
zbMATH Open document ID: 1310.32026
author: Gautam Bharali
author: Jaikrishnan Janardhanan
published in: Pacific Journal of Mathematics
publication date: 2014-11-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1302.2406
review text: Inspired by Alexander's classical result, which says that a proper holomorphic self-map of balls in multi-variables must be an automorphism, similar rigidity results have been established for bounded symmetric domains by various authors, such as Henkin and Novikov, Tsai, Tu, etc. In this paper, the authors prove that a proper holomorphic map between two equal-dimensional bounded symmetric domains in multi-variables, one of which being irreducible, must be a biholomorphism. While this result certainly generalizes previously known results, as the authors point out, the focus of the paper is rather on the method of proof, which allows them to avoid relying too heavily on the fine structure of the boundary of bounded symmetric domains. The key ingredients of the proof are Bell's extension theorem, Vigué's Schwarz lemma and Jordan triple systems. The authors also apply a similar argument to prove a similar result for non-symmetric domains with non-compact automorphism groups.
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 32H02
zbMATH DE Number: 6369626
zbMATH Keywords: bounded symmetric domains
zbMATH Keywords: proper holomorphic maps
MaRDI profile type: Publication
OpenAlex ID: W2113602624
arXiv ID: 1302.2406
DOI: 10.2140/PJM.2014.271.1
description: scientific article; zbMATH DE number 6369626