  Donaldson defined a parabolic flow on Kahler manifolds which arises from
considering the action of a group of symplectomorphisms on the space of smooth
maps between manifolds. One can define a moment map for this action, and then
consider the gradient flow of the square of its norm. Chen discovered the same
flow from a different viewpoint and called it the J-flow, since it corresponds
to the gradient flow of his J-functional, which is related to Mabuchi's
K-energy. In this paper, we show that in the case of Kahler surfaces with two
Kahler forms satisfying a certain inequality, the J-flow converges to a zero of
the moment map.
