Functions on the sphere with critical points in pairs and orthogonal geodesic chords

摘要

Using an estimate on the number of critical points for a Morse-even function on the sphere S^m, m ≥ 1, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well.