LIMITING ANGLE OF BROWNIAN-MOTION ON CERTAIN MANIFOLDS

Suppose that M is a complete, simply connected Riemannian manifold of non-positive sectional curvature with dimension m greater than or equa l to 3. If, outside a fixed compact set, the sectional curvatures are bounded above by a negative constant multiple of the inverse of the sq uare of the geodesic distance from a fixed point and below by another negative constant multiple of the square of the geodesic distance, the n the angular part of Brownian motion on M tends to a limit as time te nds to infinity, and the closure of the support of the distribution of this limit is the entire S-m-1. This improves a result of Hsu and Mar ch.