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.
Functions on the sphere with critical points in pairs and orthogonal geodesic chords
GIAMBO', Roberto;GIANNONI, Fabio;
2016-01-01
Abstract
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.File in questo prodotto:
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