On transverse hyperplanes to self-similar Jordan arcs

2013/09/02 by Tetenov, Andrey
#28A80 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1309.0332

Abstract

We consider self-similar Jordan arcs γ in R^d, different from a line segment and show that they cannot be projected to a line bijectively. Moreover, we show that the set of points x∈γ, for which there is a hyperplane, intersecting γ at the point x only, is nowhere dense in γ. .

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