  In this paper we detect new restrictions on the Maslov class of displaceable
Lagrangian submanifolds of symplectic manifolds which are symplectically
aspherical. These restrictions are established using action selectors for
Hamiltonian flows. In particular, we construct and utilize a new action
selector for the flows of a special class of Hamiltonian functions which arises
naturally in the study of Hamiltonian paths which minimize the Hofer length
functional.
