Proper holomorphic self-maps of symmetric powers of balls

2017/06/26 by Chakrabarti, Debraj, Grow, Christopher
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.08195

Abstract

We show that each proper holomorphic self map of a symmetric power of the unit ball is an automorphism naturally induced by an automorphism of the unit ball, provided the ball is of dimension at least two.

Related

• Proper holomorphic maps from the unit disk to some unit ball
• Simultaneous models for commuting holomorphic self-maps of the ball
• New examples of proper holomorphic maps among symmetric domains
• Proper holomorphic mappings of the spectral unit ball
• Local automorphisms of the Hilbert ball