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

  • Giambò R
  • Giannoni F
  • Piccione P
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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 (proved in Giambòò et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. © 2010 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Brake orbits
  • Concave boundary
  • Orthogonal geodesic chords
  • Riemannian manifolds
  • Seifert conjecture

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