Plurisubharmonically separable complex manifolds

2017/12/06 by Poletsky, Evgeny A., Shcherbina, Nikolay · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.02005

Abstract

Let M be a complex manifold and PSH^cb(M) be the space of bounded continuous plurisubharmonic functions on M. In this paper we study when 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 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 1-pseudoconcave in the sense of Rothstein sets E_j with the following Liouville property: every function from PSH^cb(M) is constant on each of E_j.

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