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Journal Articles Proceedings of the American Mathematical Society Year : 2016

On the existence of infinitely many closed geodesics on non-compact manifolds

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Abstract

We prove that any complete (and possibly non-compact) Rie-mannian manifold M possesses infinitely many closed geodesics provided its free loop space has unbounded Betti numbers in degrees larger than dim(M), and there are no close conjugate points at infinity. Our argument builds on an existence result due to Benci and Giannoni, and generalizes the celebrated theorem of Gromoll and Meyer for closed manifolds.
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Dates and versions

ensl-01520339 , version 1 (10-05-2017)

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Luca Asselle, Marco Mazzucchelli. On the existence of infinitely many closed geodesics on non-compact manifolds. Proceedings of the American Mathematical Society, 2016, 145, pp.2689 - 2697. ⟨10.1090/proc/13398⟩. ⟨ensl-01520339⟩
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