The intrinsic geometry of a Jordan domain

Details The intrinsic geometry of a Jordan domain The intrinsic geometry of a Jordan domain

2005-12-28

arxiv.org/abs/math/0512622v3

Mathematics

Differential Geometry

8 pages, 3 figures, another significant fact about the domains is stated and proved, namely, Gromov hyperbolicity

Scientific paper

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.

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