Uniqueness of shortest closed geodesics for generic Finsler metrics
  In every conformal class of Finsler (or Riemannian) metrics on a closed manifold there exists a residual subset of Finsler metrics, such that, with respect to the residual Finsler metrics, in any non-trivial homotopy class of free loops there is precisely one shortest geodesic loop. 
Jan Philipp Schr\"oder
math.DG math.DS