  A symplectic form is called hyperbolic if its pull-back to the universal
cover is a differential of a bounded one-form. The present paper is concerned
with the properties and constructions of manifolds admitting hyperbolic
symplectic forms. The main results are:
  * If a symplectic form represents a bounded cohomology class then it is
hyperbolic.
  * The symplectic hyperbolicity is equivalent to a certain isoperimetric
inequality.
  * The fundamental group of symplectically hyperbolic manifold is
non-amenable.
  We also construct hyperbolic symplectic forms on certain bundles and
Lefschetz fibrations, discuss the dependenc of the symplectic hyperbolicity on
the fundamental group and discuss some properties of the group of symplectic
diffeomorphisms of a symplectically hyperbolic manifold.

Symplectic Geometry;Geometric Topology