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Characterization of John domains via weak tangents
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Paper
Characterization of John domains via weak tangents
2026
Overview
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\\), 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 (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.
Publisher
Cornell University Library, arXiv.org
Subject
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