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Jun 22, 2014 at 3:38 comment added Daniel Pomerleano Thank you for your suggestion, Mohammed. The first reference only treats compatible complex structures, while the second indeed uses tamed almost complex structures. However, the second only studies the case of closed curves. But, hopefully, between the references and your suggestion I can figure it out.
Jun 21, 2014 at 15:19 comment added Mohammed Abouzaid The straightforward thing to do is to use Gromov's argument that such an inhomogeneous equation is equivalent to the equation for a holomorphic section of some tame almost complex structure that you can write down on the product of the surface with $M$. That of course assumes that the reference you give proves the desired result in the tame case.
Jun 21, 2014 at 14:51 history asked Daniel Pomerleano CC BY-SA 3.0