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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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:
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.