Monotonicity theorem for a J-holomorphic curve

On a compact region with controlled compatible almost complex structure, there are $c,r_0>0$ such that a nonconstant J-holomorphic curve through the center of a ball of radius $r<r_0$, with boundary outside the ball, has symplectic area at least $c{r}^2$. For the standard complex structure the sharp local constant is $\pi$.