Menger curvature and Lipschitz parametrizations in metric spaces

Immo Hahlomaa. "Menger curvature and Lipschitz parametrizations in metric spaces." Fundamenta Mathematicae 185.2 (2005): 143-169. <http://eudml.org/doc/282712>.

@article{ImmoHahlomaa2005,
abstract = {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.},
author = {Immo Hahlomaa},
journal = {Fundamenta Mathematicae},
keywords = {Menger curvature; Lipschitz parametrization; compact metric space; travelling salesman theorem},
language = {eng},
number = {2},
pages = {143-169},
title = {Menger curvature and Lipschitz parametrizations in metric spaces},
url = {http://eudml.org/doc/282712},
volume = {185},
year = {2005},
}

TY - JOUR
AU - Immo Hahlomaa
TI - Menger curvature and Lipschitz parametrizations in metric spaces
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 2
SP - 143
EP - 169
AB - 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.
LA - eng
KW - Menger curvature; Lipschitz parametrization; compact metric space; travelling salesman theorem
UR - http://eudml.org/doc/282712
ER -