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arXiv · 2011.04831

A Jordan Curve that cannot be Crossed by Rectifiable Arcs on a Set of Zero Length

Jack Burkart
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Abstract

We construct a Jordan curve $\Gamma \subset \mathbb{C}$ so that for any rectifiable arc $\sigma$ with endpoints in distinct complementary components of $\Gamma$, $H^1(\sigma \cap \Gamma) > 0$.

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Jack Burkart. 2020-11-09. A Jordan Curve that cannot be Crossed by Rectifiable Arcs on a Set of Zero Length. https://arxiv.org/abs/2011.04831

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