  In this paper we make the first steps towards developing a theory of
intersections of coisotropic submanifolds, similar to that for Lagrangian
submanifolds.
  For coisotropic submanifolds satisfying a certain stability requirement we
establish persistence of coisotropic intersections under Hamiltonian
diffeomorphisms, akin to the Lagrangian intersection property. To be more
specific, we prove that the displacement energy of a stable coisotropic
submanifold is positive, provided that the ambient symplectic manifold meets
some natural conditions. We also show that a displaceable, stable, coisotropic
submanifold has non-zero Liouville class. This result further underlines the
analogy between displacement properties of Lagrangian and coisotropic
submanifolds.
