  We introduce a vector bundle version of the complex Monge-Ampere equation
motivated by a desire to study stability conditions involving higher Chern
forms. We then restrict ourselves to complex surfaces, provide a moment map
interpretation of it, and define a positivity condition (MA positivity) which
is necessary for the infinite-dimensional symplectic form to be Kahler. On
rank-2 bundles on compact complex surfaces, we prove two consequences of the
existence of a "positively curved" solution to this equation - Stability
(involving the second Chern character) and a
Kobayashi-Lubke-Bogomolov-Miyaoka-Yau type inequality. Finally, we prove a
Kobayashi-Hitchin correspondence for a dimensional reduction of the
aforementioned equation.
