Menger curvature and Lipschitz parametrizations in metric spaces

• Autorzy: Immo Hahlomaa
• Języki publikacji: EN

Abstrakty

EN

We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.

Kategorie tematyczne

• 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions
• 51F99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 185
• Numer: 2
• Strony: 143-169

Daty

wydano

2005

Twórcy

autor

Immo Hahlomaa

• Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40014 Jyväskylä, Finland

Identyfikatory

DOI

10.4064/fm185-2-3