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Geodesics avoiding subsets in Hadamard manifolds


Author: Albert Borbély
Journal: Proc. Amer. Math. Soc. 138 (2010), 1085-1092
MSC (2000): Primary 53C22
DOI: https://doi.org/10.1090/S0002-9939-09-10095-3
Published electronically: October 23, 2009
MathSciNet review: 2566573
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-09-10095-3
Keywords: Convex sets, negative curvature, geodesics
Received by editor(s): June 12, 2008
Published electronically: October 23, 2009
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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