Plurisubharmonic exhaustion functions and almost complex Stein structures

2006/03/17 by Klas Diederich, Diederich, Klas, Alexandre Sukhov +1
Mathematics · #Geometric and Algebraic Topology #Advanced Operator Algebra Research #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/0603417

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.

Citations

• Symplectic manifolds with contact type boundaries

Related

• Domains with a continuous exhaustion in weakly complete surfaces
• Some aspects of analysis on almost complex manifolds with boundary
• Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions
• Approximation and Bounded Plurisubharmonic Exhaustion Functions Beyond Lipschitz Domains
• Gromov hyperbolicity of strongly pseudoconvex almost complex manifolds