Poletsky theory of discs in almost complex manifolds

We prove the existence of a maximal plurisubharmonic minorant of a given upper semicontinous function f on an almost complex manifold (M, J) of complex dimension two. Such maximal function is obtained as the pointwise minimum of averages of f over the boundaries of all J-complex discs in M centered at the given point. This result is an almost complex analogue of classical results of Poletsky, Larusson and Sigurdsson, Rosay and others in the case when the almost complex structure J is integrable.