Length spectrum of geodesic loops in manifolds of nonpositive curvature (1103.4157v1)

Abstract: In section 1 we reformulate a theorem of Blichfeldt in the framework of manifolds of nonpositive curvature. As a result we obtain a lower bound on the number of homotopically distinct geodesic loops emanating from a common point q whose length is smaller than a fixed constant. This bound depends only on the volume growth of balls in the universal covering and the volume of the manifold itself. We compare the result with known results about the asymptotic growth rate of closed geodesics and loops in section 2.