On compact subsets possessing strictly plurisubharmonic functions

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.

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Bibliographic Details
Published inIzvestiya. Mathematics Vol. 85; no. 3; pp. 605 - 618
Main Author Shcherbina, N. V.
Format Journal Article
LanguageEnglish
Published Providence London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.06.2021
IOP Publishing
Subjects
1$-pseudoconcave sets
Harmonic functions
strictly plurisubharmonic functions
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Summary: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.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM9059