Characterization of John domains via weak tangents
Complex Variables
2026-02-24 v2 Metric Geometry
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 is a John domain if and only if, for every weak tangent of , every connected component of the complement of that ``originates" from is a John domain, not necessarily with uniform constants. Our main theorem improves a result of Kinneberg (arXiv:1507.04698), 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.
Cite
@article{arxiv.2501.18425,
title = {Characterization of John domains via weak tangents},
author = {Christina Karafyllia},
journal= {arXiv preprint arXiv:2501.18425},
year = {2026}
}
Comments
17 pages, 1 figure