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Characterization of compact subsets of curves with ω-continuous derivatives

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Pilipczuk M.

Fundamenta Mathematicae

2011

tom 211

nr 2

175-195

We give a characterization of compact subsets of finite unions of disjoint finite-length curves in ℝⁿ with ω-continuous derivative and without self-intersections. Intuitively, our condition can be formulated as follows: 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 characterize compact subsets of rectifiable or Ahlfors-regular curves. However, their classes of curves are much wider than ours and therefore the condition we obtain and our methods are different.

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1 Fundamenta Mathematicae

1 Pilipczuk M.

1 2011

Wyniki wyszukiwania

Characterization of compact subsets of curves with ω-continuous derivatives