Almost global existence for Hamiltonian semi-linear Klein-Gordon   equations with small Cauchy data on Zoll manifolds
  This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on Zoll manifolds. 
Dario Bambusi, Jean-Marc Delort (LAGA), Benoit Grebert (LMJL), Jeremie   Szeftel (MAB)