A note on exhaustion of hyperbolic complex manifolds

2020/06/06 by Ninh Van Thu, Van Thu, Ninh, Trinh Huy Vu +1
Mathematics · #32H02 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32H02

paper · pdf · doi:10.48550/arxiv.2006.03821

All comments are welcome

arxiv created 2020/06/06 · arxiv updated 2020/06/09

Abstract

The purpose of this article is to investigate a hyperbolic complex manifold M exhausted by a pseudoconvex domain Ω in \mathbb Cⁿ via an exhausting sequence \f_j\colon Ω→ M\ such that f_j^-1(a) converges to a boundary point ξ₀ ∈ ∂ Ω for some point a∈ M.

Related

• Exhaustion of hyperbolic complex manifolds and relations to the squeezing function
• Plurisubharmonic exhaustion functions and almost complex Stein structures
• Limits of an increasing sequence of complex manifolds
• Propagation of regularity for Monge-Ampère exhaustions and Kobayashi metrics
• Characterizations of convergence by a given set of angles in simply connected domains