Upper Bounds on the Length of a Shortest Closed Geodesic and QuantitativeHurewicz Theorem

摘要

In this paper we present two upper bounds on the length of a shortest closedgeodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of a manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the diameter and a lower bound on the volume.