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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 distinctdoi:10.2140/gt.2007.11.1225 fatcat:kqxkohffjvfr5d7n62w6sdixqy