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

  • Giambò R
  • Giannoni F
  • Piccione P
  • 4


    Mendeley users who have this article in their library.
  • 8


    Citations of this article.


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

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free