Resonance for loop homology of spheres

@article{Hingston2011ResonanceFL,
  title={Resonance for loop homology of spheres},
  author={Nancy Hingston and Hans Rademacher},
  journal={arXiv: Differential Geometry},
  year={2011}
}
A Riemannian or Finsler metric on a compact manifold M gives rise to a length function on the free loop space \Lambda M, whose critical points are the closed geodesics in the given metric. If X is a homology class on \Lambda M, the minimax critical level cr(X) is a critical value. Let M be a sphere of dimension >2, and fix a metric g and a coefficient field G. We prove that the limit as deg(X) goes to infinity of cr(X)/deg(X) exists. We call this limit the "global mean frequency" of M. As a… 
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The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $$S^{2n+1}/ \Gamma $$S2n+1/Γ
  • Hui Liu
  • Mathematics
    Calculus of Variations and Partial Differential Equations
  • 2019
Let $$M=S^{2n+1}/ \Gamma $$M=S2n+1/Γ, $$\Gamma $$Γ is a finite group which acts freely and isometrically on the $$(2n+1)$$(2n+1)-sphere and therefore M is diffeomorphic to a compact space form. In
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