Sui Chung Ng, HKU, Hong Kong

Proper holomorphic maps on bounded symmetric domains of rank at least 2 and characteristic symmetric subspaces

Abstract

In an early work of Mok and Tsai in 1992 regarding the rigidity of convex realizations of bounded symmetric domains, it has been shown that proper holomorphic maps between bounded symmetric domains of rank at least 2 preserve certain symmetric subspaces, known as characteristic symmetric subspaces. This property has then been further exploited by Tsai and Tu in their studies of proper holomorphic maps between bounded symmetric domains. In this talk, we will first briefly introduce the related notions and then we will discuss a recent joint work with Mok and Tu regarding arbitrary proper holomorphic maps defined on an irreducible bounded symmetric domain (with rank ³ 2) and a simple proof of Tsai's theorem on proper holomorphic maps between domains of equal rank.