Characterization of compact subsets of curves with ω-continuous derivatives
نویسنده
چکیده
In this paper we focus on characterizing compact subsets of curves in R with regular derivatives. Namely, we give characterization of compact subsets of finite sums of disjoint finite-length curves with ω-continuous derivative and without selfintersections. Intuitively, our condition can be formulated as there exists a finite set of regular curves covering a compact set K iff every triple of points of K behaves like a triple of points of a regular curve. This work was inspired by theorems by Jones, Okikiolu, Schul and others that characterized compact subsets of rectifiable or Ahlfors-regular curves. However, their classes of curves are much wider that ours and therefore the obtained condition and our methods are different. AMS classification: 53A04 Curves in Euclidean space.
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