G. Contreras, J. Delgado, R. Iturriaga
Lagrangian Flows:   The Dynamics of  Globally Minimizing Orbits - II
(100K, LaTeX)

ABSTRACT.  Define the critical level c(L) of a convex superlinear autonomous
Lagrangian L as the infimum of the k's such that the Lagrangian L+k 
has minimizers with fixed endpoints and free time interval. We provide 
proofs for Mañé's statements characterizing c(L) in terms of minimizing 
measures for L, and also giving graph, recurrence, covering and 
cohomology properties for minimizers of L+c(L). It is also proven 
that the minimizers of L+c(L) are in the  energy level E=c(L) and 
that c(L) is the infimum of the energy levels k such that the
following form of Tonelli's theorem holds: there exist minimizers 
of the (L+k)-action joining any two points in the projection of 
E=k among curves with energy k.