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The intrinsic geometry of a Jordan domain

Richard L. Bishop
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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.

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Richard L. Bishop. 2007-07-23. The intrinsic geometry of a Jordan domain. https://arxiv.org/abs/math/0512622

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