Geodesic
Menger curvature and Lipschitz parametrizations in metric spaces
Immo Hahlomaa1
1 Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 FIN-40014 Jyväskylä, Finland
Fundamenta Mathematicae, Tome 185 (2005) no. 2, pp. 143-169.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\Omega(\varepsilon)$, the class of bounded metric spaces $E$ such that the maximum angle for every triple in $E$ is at least $\pi/2 + \arcsin\varepsilon$. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.
DOI : 10.4064/fm185-2-3
Keywords: pointwise bounds menger curvature imply lipschitz parametrization general compact metric spaces estimates optimal lipschitz constants parametrizing maps metric spaces omega varepsilon class bounded metric spaces maximum angle every triple least arcsin varepsilon finally extend peter joness travelling salesman theorem general metric spaces

Immo Hahlomaa 1

1 Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 FIN-40014 Jyväskylä, Finland 
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Immo Hahlomaa. Menger curvature and Lipschitz parametrizations in metric spaces. Fundamenta Mathematicae, Tome 185 (2005) no. 2, pp. 143-169. doi : 10.4064/fm185-2-3. http://geodesic.mathdoc.fr/articles/10.4064/fm185-2-3/

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