Invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces

2019/12/09 by Geatti, Laura, Iannuzzi, Andrea
#31C10 #32M15 #32T05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.03975

Abstract

Let G/K be an irreducible Hermitian symmetric space and let D be a K-invariant domain in G/K. In this paper we characterize several classes of K-invariant plurisubharmonic functions on D in terms of their restrictions to a slice intersecting all K-orbits. As applications we show that K-invariant plurisubharmonic functions on D are necessarily continuous and we reproduce the classification of Stein K-invariant domains in G/K obtained by E. Bedford and J. Dadok.

Related

• Geometry of Hermitian symmetric spaces under the action of a maximal unipotent group
• Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem
• Invariant envelopes of holomorphy in the complexification of a Hermitian symmetric space
• Graham Theorem on Bounded Symmetric Domains
• A Survey on Invariant Spaces of Holomorphic Functions on Symmetric Domains