Invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces

TL;DR

This paper characterizes K-invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces, showing their continuity and reproducing known classifications of Stein domains through restriction analysis.

Contribution

It provides a new characterization of K-invariant plurisubharmonic functions via their restrictions to slices, extending understanding of their properties on Hermitian symmetric spaces.

Findings

K-invariant plurisubharmonic functions are necessarily continuous

Reproduces classification of Stein K-invariant domains in G/K

Characterizes functions via restrictions to slices intersecting all K-orbits

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.