Length spectrum of geodesic loops in manifolds of non-positive curvature (Q1990608)

Suppose that \(M\) is a complete Riemannian manifold of non-positive curvature and finite volume. Then the number of homotopically distinct geodesic loops based at some point \(q\) in \(M\) which have length less than or equal to a fixed number \(t\) is bounded from below by the volume of \(M\) and the volume of the geodesic ball of radius \(t/2\) in the universal cover of \(M\). This result is obtained as a corollary of a generalization of a theorem of Blichfeldt that is also proved in this paper.