Hyperbolicity and chain recurrence
β Scribed by John E. Franke; James F. Selgrade
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 540 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature K are integrable. This last condition is required only for the tracef
We give an estimate for the distance functions related to the Bergman, Carathkodory, and Kobayashi metrics on a bounded strictly pseudoconvex domain with C'-smooth boundary. Our formula relates the distance function on the domain with the Carnot-Carathkodory metric on the boundary. As a corollary we
If X is a geodesic metric space and x 1 , x 2 , x 3 β X , a geodesic triangle T = {x 1 , x 2 , x 3 } is the union of the three geodesics [x 1 x 2 ], [x 2 x 3 ] and [x 3 x 1 ] in X . The space X is Ξ΄-hyperbolic (in the Gromov sense) if any side of T is contained in a Ξ΄-neighborhood of the union of th