Abstract
Let (M,g) be a complete Riemannian manifold, and let \({\Omega \subset M}\) be an open subset whose closure is homeomorphic to a disk or to an annulus. In this note we discuss some multiplicity results for orthogonal geodesic chords in \({\bar{\Omega}}\), namely geodesics in \({\bar{\Omega}}\) starting from and arriving orthogonally to the boundary of \({\Omega}\). This kind of problems has applications to multiplicity results for brake orbits and homoclinics, via Maupertuis principle.
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Giambò, R., Giannoni, F. & Piccione, P. Multiplicity results for orthogonal geodesic chords and applications. J. Fixed Point Theory Appl. 16, 259–272 (2014). https://doi.org/10.1007/s11784-014-0204-1
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DOI: https://doi.org/10.1007/s11784-014-0204-1