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

Abstract

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.

arXiv comment59 pages, 3 figures. To appear on Nonlinear Analysis Series A: Theory, Methods & Applications

Cited by in corpus (3)

• Multiple orthogonal geodesic chords and a proof of Seifert's conjecture on brake orbits
• Morse Theory for geodesics in singular conformal metrics
• Brake orbits for Hamiltonian systems of classical type via Finsler geodesics