Proper holomorphic maps between bounded symmetric domains revisited

Abstract

We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively.

arXiv comment19 pages; typos corrected; missing hypothesis added to the statement of Lemma 4.2; to appear in Pacific J. Math

Cited by in corpus (2)

• Proper holomorphic mappings of balanced domains in ${\mathbb{C}}^n$
• Carathéodory distance-preserving maps between bounded symmetric domains