Characterization of compact subsets of curveswith w-continuous derivatives

摘要

We give a characterization of compact subsets of finite unions of disjoint finite-length curves in R~n with -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 char-acterize compact subsets of rectifiable or Ahifors-regular curves. However, their classes of curves are much wider than ours and therefore the condition we obtain and our methods are different.