English

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 DD is a John domain if and only if, for every weak tangent YY of D\partial D, every connected component of the complement of YY that ``originates" from DD 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.

Keywords

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