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A minimal geodesic on a Riemannian manifold is a geodesic defined on$\mathbb{R}$ that lifts to a globally distance minimizing curve on theuniversal covering. Bangert proved that there is a lower bound for the numberof geometrically distinct minimal geodesics of closed Riemannian manifolds thatis linear in the first Betti number, using the stable norm unit ball on thefirst homology. We refine this method to obtain a quadratic lower bound.

A quadratic lower bound for the number of minimal geodesics