The intrinsic geometry of a Jordan domain
arXiv:math/0512622
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.
8 pages, 3 figures, another significant fact about the domains is stated and proved, namely, Gromov hyperbolicity