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PLURIPOLAR SETS, REAL SUBMANIFOLDS AND PSEUDOHOLOMORPHIC DISCS

Part of: Holomorphic mappings and correspondences Global differential geometry

Published online by Cambridge University Press:  08 April 2019

ALEXANDRE SUKHOV
ALEXANDRE SUKHOV*
Affiliation:
Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé, U.F.R. de Mathématique, 59655 Villeneuve d’Ascq, Cedex, France Institut of Mathematics with Computing Centre,Subdivision of the Ufa Research Centre of Russian Academy of Sciences, 45008, Chernyshevsky Str. 112, Ufa, Russia email [email protected]
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Abstract

We prove that a compact subset of full measure on a generic submanifold of an almost complex manifold is not a pluripolar set. Several related results on boundary behavior of plurisubharmonic functions are established. Our approach is based on gluing a family of complex discs to a generic manifold along a boundary arc and could admit further applications.

Keywords

almost complex structureplurisubharmonic functionpseudoholomorphic disctotally real manifold

MSC classification

Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 109 , Issue 2 , October 2020 , pp. 270 - 288
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

The author is partially supported by Labex CEMPI.

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