Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Geodesics avoiding subsets in Hadamard manifolds


Author: Albert Borbély
Journal: Proc. Amer. Math. Soc. 138 (2010), 1085-1092
MSC (2000): Primary 53C22
Published electronically: October 23, 2009
MathSciNet review: 2566573
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C22

Retrieve articles in all journals with MSC (2000): 53C22


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: http://dx.doi.org/10.1090/S0002-9939-09-10095-3
PII: S 0002-9939(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.