Year: 2026
Type: preprint
Abstract: We prove that every bounded pseudoconvex domain in $\mathbb C^N$ with $C^\infty$ boundary of finite D'Angelo one-type is Kobayashi complete. As a separate consequence of our criterion of completeness and an estimate of Diederich--Fornæss, we prove that every bounded pseudoconvex domain with real-analytic boundary is Kobayashi complete. We then show that smoothness alone does not imply completeness: there exists a bounded pseudoconvex domain in $\mathbb C^3$ with $C^\infty$ boundary and a global smooth plurisubharmonic defining function whose Kobayashi and Carathéodory distances are incomplete.
Source: arXiv (Cornell University)
Author: Edigarian, Armen
Institution: Jagiellonian University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223215761