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Quasigeodesics outside horoballs


Let Ω be the path metric space obtained from a Hadamard manifold X by removing a collection of pairwise disjoint open horoballs from X. In case X is a rank one symmetric space, certain properties of quasigeodesics in Ω have been used to derive results about lattices in X. For two such properties we give new proofs that simultaneously apply to the case where X is a Hadamard space with sectional curvature -a 2K≤-1,1≤a<2. In this case, as an application of one of these properties, we show that every lattice in X is biautomatic.

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Lang, U. Quasigeodesics outside horoballs. Geom Dedicata 63, 205–215 (1996).

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