a1 Courant Institute for Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
Let M be a compact Riemannian manifold of (variable) negative curvature. Let h be the topological entropy and hμ the measure entropy for the geodesic flow on the unit tangent bundle to M. Estimates for h and hμ in terms of the ‘geometry’ of M are derived. Connections with and applications to other geometric questions are discussed.
(Received August 22 1981)