Menger curvature and Lipschitz parametrizations in metric spaces
Fundamenta Mathematicae, Tome 185 (2005) no. 2, pp. 143-169
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
Immo Hahlomaa 1
@article{10_4064_fm185_2_3,
author = {Immo Hahlomaa},
title = {Menger curvature and {Lipschitz} parametrizations in metric spaces},
journal = {Fundamenta Mathematicae},
pages = {143--169},
year = {2005},
volume = {185},
number = {2},
doi = {10.4064/fm185-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm185-2-3/}
}
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
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