The isometry groups of manifolds of nonpositive curvature with finite volume (Q760024)

Let M be a complete Riemannian manifold with finite volume, sectional curvature \(-\Lambda^ 2\leq K\leq 0\) and negative definite Ricci tensor at some point. Then the isometry group I(M) of M is finite; see \textit{G. Avérous} and \textit{S. Kobayashi} [Differ. Geom. Relativ., Vol. Honour A. Lichnerowicz 60th Birthday, 19-26 (1976; Zbl 0366.53025)]. Assume that M' is a bounded open submanifold of M with finite diameter d(M') which is a deformation retract of M. Then the order of I(M) is estimated from above in terms of \(\Lambda\), d(M'), dim(M) and the infimum of the injectivity radius \(i_ M(p)\) on M'.