Shapes of geodesic nets

Alexander Nabutovsky, Regina Rotman
2007 Geometry and Topology  
Let M n be a closed Riemannian manifold of dimension n. In this paper we will show that either the length of a shortest periodic geodesic on M n does not exceed .n C 1/d , where d is the diameter of M n or there exist infinitely many geometrically distinct stationary closed geodesic nets on this manifold. We will also show that either the length of a shortest periodic geodesic is, similarly, bounded in terms of the volume of a manifold M n , or there exist infinitely many geometrically distinct
more » ... metrically distinct stationary closed geodesic nets on M n .
doi:10.2140/gt.2007.11.1225 fatcat:kqxkohffjvfr5d7n62w6sdixqy