A quadratic lower bound for the number of minimal geodesics
by
Bernd Ammann, Clara Löh
A quadratic lower bound for the number of minimal geodesics,
Preprint version (pdf)
Abstract
A minimal geodesic on a Riemannian manifold is a geodesic defined on ℝ that lifts to a globally distance minimizing curve on the universal covering. Bangert proved that there is a lower bound for the number of geometrically distinct minimal geodesics of closed Riemannian manifolds that is linear in the first Betti number, using the stable norm unit ball on the first homology. We refine this method to obtain a quadratic lower bound.
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Last update of this page 11.04.2024
The paper was originally written on 2.11.2023