Asymptotic invariants of Hadamard manifolds

We study various asymptotic invariants of manifolds of nonpositive curvature. First, we study the filling invariants at infinity divk for Hadamard manifolds defined by Noel Brady and Benson Farb. Among other results, we give a positive answer to the question they posed: can these invariants be used to detect the rank of a symmetric space of noncompact type? Second, we study the asymptotic cones of the universal covers of 4-dimensional closed nonpositively curved real analytic manifolds. We show that the existence of nonstandard components in the Tits boundary, discovered by Christoph Hummel and Victor Schroeder, depends only on the quasi-isometry type of the fundamental group