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Geodesics avoiding subsets in Hadamard manifolds
Author(s):
Albert
Borbély
Journal:
Proc. Amer. Math. Soc.
MSC (2000):
Primary 53C22
Posted:
October 23, 2009
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Abstract:
Let  ,  , be an  -hyperbolic (in the sense of Gromov) Hadamard manifold. Let us assume that we are given a family of disjoint convex subsets and a point  outside these sets. It is shown that if one shrinks these sets by the constant  , then it is possible to find a complete geodesic through  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:
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
Posted:
October 23, 2009
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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