Year: 2026
Type: article
Abstract: We characterize simply connected John domains in the plane with the aid of weak tangents of the boundary. Specifically, we prove that a bounded simply connected domain D is a John domain if and only if, for every weak tangent Y of $$\partial D$$ ∂ D , every connected component of the complement of Y that “originates” from D is a John domain, not necessarily with uniform constants. Our main theorem improves a result of Kinneberg (Trans. Amer. Math. Soc. 369 (9), 6511–6536, 2017), who obtains a necessary condition for a John domain in terms of weak tangents but not a sufficient one. We also establish several properties of weak tangents of John domains.
Source: Potential Analysis
Author: Christina Karafyllia
Institution: University of Western Macedonia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: University of Western Macedonia
Award: G8688368115
OpenAlex ID: W7130860220