Geodesics avoiding subsets in Hadamard manifolds

Borbély, Albert

doi:10.1090/S0002-9939-09-10095-3

Geodesics avoiding subsets in Hadamard manifolds
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by Albert Borbély PDF

Proc. Amer. Math. Soc. 138 (2010), 1085-1092 Request permission

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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