QUASIFLATS IN HADAMARD SPACES

Let X be a simply connected, complete geodesic metric space which is n onpositively curved in the sense of Alexandrov. We assume that X conta ins a k-flat F of maximal dimension and consider quasiisometric embedd ings f:R-k --> X whose distance function from F satisfies a certain as ymptotic growth condition. We prove that if X is locally compact and c ocompact, then the Hausdorff distance between f(R-k) and F is uniforml y bounded. This generalizes a well-known lemma of Mostow on quasiflats in symmetric spaces of noncompact type.