English

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

Complex Variables 2020-11-11 v1 Metric Geometry

Abstract

We construct a Jordan curve ΓC\Gamma \subset \mathbb{C} so that for any rectifiable arc σ\sigma with endpoints in distinct complementary components of Γ\Gamma, H1(σΓ)>0H^1(\sigma \cap \Gamma) > 0.

Keywords

Cite

@article{arxiv.2011.04831,
  title  = {A Jordan Curve that cannot be Crossed by Rectifiable Arcs on a Set of Zero Length},
  author = {Jack Burkart},
  journal= {arXiv preprint arXiv:2011.04831},
  year   = {2020}
}

Comments

25 pages, 14 Figures