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arXiv · 1712.02005

Plurisubharmonically separable complex manifolds

Evgeny A. Poletsky·Nikolay Shcherbina
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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 $w_0\in M$ there is a continuous plurisubharmonic function $u$ with the logarithmic singularity at $w_0$. Moreover, the core of $M$ is the disjoint union of 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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Evgeny A. Poletsky, Nikolay Shcherbina. 2017-12-06. Plurisubharmonically separable complex manifolds. https://arxiv.org/abs/1712.02005

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