On the existence of infinitely many closed geodesics on non-compact manifolds
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- by Luca Asselle and Marco Mazzucchelli PDF
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Abstract:
We prove that any complete (and possibly non-compact) Riemannian manifold $M$ possesses infinitely many closed geodesics provided its free loop space has unbounded Betti numbers in degrees larger than $\mathrm {dim}(M)$ 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.References
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Additional Information
- Luca Asselle
- Affiliation: Ruhr Universität Bochum, Fakultät für Mathematik, Gebäude NA 4/33, D-44801 Bochum, Germany
- MR Author ID: 1125943
- Email: luca.asselle@ruhr-uni-bochum.de
- Marco Mazzucchelli
- Affiliation: CNRS, École Normale Supérieure de Lyon, UMPA, 69364 Lyon Cedex 07, France
- MR Author ID: 832298
- Email: marco.mazzucchelli@ens-lyon.fr
- Received by editor(s): April 28, 2016
- Received by editor(s) in revised form: July 21, 2016, and July 22, 2016
- Published electronically: November 30, 2016
- Additional Notes: The first author was partially supported by the DFG grant AB 360/2-1, “Periodic orbits of conservative systems below the Mañé critical energy value”
The second author was partially supported by the ANR projects WKBHJ (ANR-12-BS01-0020) and COSPIN (ANR-13-JS01-0008-01) - Communicated by: Guofang Wei
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2689-2697
- MSC (2010): Primary 53C22, 58E10
- DOI: https://doi.org/10.1090/proc/13398
- MathSciNet review: 3626521