Fiberwise Convexity of Hill's lunar problem
  In this paper, I prove the fiberwise convexity of the regularized Hill's lunar problem below the critical energy level. This allows us to see Hill's lunar problem of any energy level below the critical value as the Legendre transformation of geodesic problem on $S^2$ with a family of Finsler metric. 
Lee Junyoung
math.SG