Plurisubharmonic exhaustion functions and almost complex Stein structures

Klas Diederich; Alexandre Sukhov

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Plurisubharmonic exhaustion functions and almost complex Stein structures

Klas Diederich·Alexandre Sukhov

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Abstract

We prove that a relatively compact pseudoconvex domain with smooth boundary in an almost complex manifold admits a bounded strictly plurisubharmonic exhaustion function. We use this result for the study of convexity and hyperbolicity properties of these domains and the contact geometry of their boundaries.

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Klas Diederich, Alexandre Sukhov. 2006-03-17. Plurisubharmonic exhaustion functions and almost complex Stein structures. https://arxiv.org/abs/math/0603417

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