This article is cited in 5 papers

On compact subsets possessing strictly plurisubharmonic functions

N. V. Shcherbina

Department of Mathematics, University of Wuppertal, Wuppertal, Germany

Abstract: We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.

Keywords: strictly plurisubharmonic functions, $1$-pseudoconcave sets.

UDC: 517.576

MSC: Primary 32U05; Secondary 32Q99

Received: 28.04.2020
Revised: 03.08.2020

DOI: 10.4213/im9059

 English version: Izvestiya: Mathematics, 2021, 85:3, 605–618

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