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 (proved in Giambòò et al. (2005) ) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) ) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. © 2010 Elsevier Ltd. All rights reserved.
Giambò, R., Giannoni, F., & Piccione, P. (2010). Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk. Nonlinear Analysis, Theory, Methods and Applications, 73(2), 290–337. https://doi.org/10.1016/j.na.2010.03.019