## Abstract

Let M be a complex manifold and let PSH^{cb} (M) be the space of bounded continuous plurisubharmonic functions on M. In this paper we study when the functions from PSH^{cb} (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 w_{0} ∈ M there is a continuous plurisubharmonic function u with the logarithmic singularity at w_{0}. Moreover, the core of M is the disjoint union of the sets E_{j} that are 1-pseudoconcave in the sense of Rothstein and have the following Liouville property: every function from PSH^{cb} (M) is constant on each E_{j}.

Original language | English (US) |
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Pages (from-to) | 2413-2424 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 6 |

DOIs | |

State | Published - 2019 |

## Keywords

- Bounded plurisubharmonic functions
- Cores of domains

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics