Length spectrum of geodesic loops in manifolds of nonpositive curvature

Details Length spectrum of geodesic loops in manifolds of nonpositive curvature Length spectrum of geodesic loops in manifolds of nonpositive curvature

2011-03-21

arxiv.org/abs/1103.4157v1

Mathematics

Geometric Topology

4 pages

Scientific paper

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.

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