Characterization of compact subsets of curves with ω-continuous derivatives

• Autorzy: Marcin Pilipczuk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53A04: Curves in Euclidean space

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 2
• Strony: 175-195

Daty

wydano

2011

Twórcy

autor

Marcin Pilipczuk

• Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm211-2-4