Plurisubharmonically separable complex manifolds

Evgeny Alexander Poletsky, Nikolay Shcherbina

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2413-2424
Number of pages12
JournalProceedings of the American Mathematical Society
Volume147
Issue number6
DOIs
StatePublished - Jan 1 2019

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Complex Manifolds
Plurisubharmonic Function
Continuous Function
Logarithmic
Disjoint
Union
Singularity

Keywords

  • Bounded plurisubharmonic functions
  • Cores of domains

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Plurisubharmonically separable complex manifolds. / Poletsky, Evgeny Alexander; Shcherbina, Nikolay.

In: Proceedings of the American Mathematical Society, Vol. 147, No. 6, 01.01.2019, p. 2413-2424.

Research output: Contribution to journalArticle

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