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math.DG2005
Lengths of geodesics between two points on a Riemannian manifold
Alexander Nabutovsky, Regina Rotman
Let x and y be two (not necessarily distinct) points on a closed Riemannian manifold M of dimension n. According to a celebrated theorem by J.P. Serre there exist infinitely many g…
math.DG2002
Volume, diameter and the minimal mass of a stationary 1-cycle
Alexander Nabutovsky, Regina Rotman
In this paper we present upper bounds on the minimal mass of a non-trivial stationary 1-cycle. The results that we obtain are valid for all closed Riemannian manifolds. The first r…