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.
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