Quasigeodesics outside horoballs (Q1815265)

Let \(X\) be a Hadamard manifold which is a rank one symmetric space and \(\Omega\) be the path metric space obtained from \(X\) by removing a collection of pairwise disjoint open horoballs from \(X\). By using certain properties of quasigeodesics in \(\Omega\) some results about lattices in \(X\) can be obtained. In this paper, for two such properties the author gives new proofs that simultaneously apply to the case where \(X\) is a Hadamard space with sectional curvature \(-a^2\leq K\leq -1\), \(1\leq a<2\). One of these properties is applied to show that every lattice in \(X\) is biautomatic.