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

2020/11/09 by Burkart, Jack
#54F50 #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2011.04831

Abstract

We construct a Jordan curve Γ⊂ ℂ so that for any rectifiable arc σ with endpoints in distinct complementary components of Γ, H¹(σ∩ Γ) > 0.

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