Let M be a complex manifold and let PSHcb (M) be the space of bounded continuous plurisubharmonic functions on M. In this paper we study when the functions from PSHcb (M) separate points. Our main results show that this property is equivalent to each of the following properties of M: (1) the core of M is empty; (2) for every w0 ∈ M there is a continuous plurisubharmonic function u with the logarithmic singularity at w0. Moreover, the core of M is the disjoint union of the sets Ej that are 1-pseudoconcave in the sense of Rothstein and have the following Liouville property: every function from PSHcb (M) is constant on each Ej.
- Bounded plurisubharmonic functions
- Cores of domains
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics