The intrinsic geometry of a Jordan domain
Differential Geometry
2007-07-23 v3
Abstract
For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a CAT(0)space and Gromov hyperbolic. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.
Cite
@article{arxiv.math/0512622,
title = {The intrinsic geometry of a Jordan domain},
author = {Richard L. Bishop},
journal= {arXiv preprint arXiv:math/0512622},
year = {2007}
}
Comments
8 pages, 3 figures, another significant fact about the domains is stated and proved, namely, Gromov hyperbolicity