Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

Details Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

2010-03-19

arxiv.org/abs/1003.3846v1

Mathematics

Dynamical Systems

59 pages, 3 figures. To appear on Nonlinear Analysis Series A: Theory, Methods & Applications

Scientific paper

In this paper we give a proof of the existence of an orthogonal geodesic
chord on a Riemannian manifold homeomorphic to a closed disk and with concave
boundary. This kind of study is motivated by the link of the multiplicity
problem with the famous Seifert conjecture (formulated in 1948) about multiple
brake orbits for a class of Hamiltonian systems at a fixed energy level.

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