Geodesics avoiding subsets in Hadamard manifolds
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- by Albert Borbély PDF
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Abstract:
Let $M^{n}$, $n\geq 3$, be an $s$-hyperbolic (in the sense of Gromov) Hadamard manifold. Let us assume that we are given a family of disjoint convex subsets and a point $o$ outside these sets. It is shown that if one shrinks these sets by the constant $s$, then it is possible to find a complete geodesic through $o$ that avoids the shrunk sets.References
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Additional Information
- Albert Borbély
- Affiliation: Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
- Email: borbely.albert@gmail.com
- Received by editor(s): June 12, 2008
- Published electronically: October 23, 2009
- Communicated by: Jon G. Wolfson
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1085-1092
- MSC (2000): Primary 53C22
- DOI: https://doi.org/10.1090/S0002-9939-09-10095-3
- MathSciNet review: 2566573