复流形或解析空间上闭，正(p,p)流(closed positive (p,p) currents)的光滑性已有了广泛深入研究。如何分析近复流形上闭，正(p,p)流的正则性尚未不知。假如近复流形具有局部辛性质，那么通过Darboux定理我们可以在流形局部使用Darboux坐标卡。这样一来我们可以认为具有局部辛性质的近复流形是复流形的推广。在Eliashberg和Gromov考虑了辛流形的凸性和Elkhadhra在近复流形上定义了Lelong数和J-解析子集后，我们认为在近复流形上也可以考虑闭的正(p,p)型流的正则性和奇点。假设(M,J)具有局部辛性质或是近Kaehler的。为了研究这类近复流形上闭，正(p,p)流的奇异性，我们引入Donaldson在研究辛子流形时开创的全纯逼近方法。然后期望得到Demailly和Siu在复流形上类似的结果。

Extensive research about the smoothness of closed positive (p,p) currents on complex manifold has been carried out. However, such research is very lack on almost complex manifold. Suppose that the almost complex manifold has local symplectic property. By Darboux theorem, we can establish Darboux coordinate system on it. Then we consider the almost complex manifold with local symplectic property as the generalization of complex manifold. Elkhadhra defined Lelong number and J-analytic subset on almost complex manifold. After Eliashberg and Gromov studying the convexity of symplectic manifolds, we think we can study the smoothness of closed positive (p,p) currents on almost complex manifold with local symplectic property. By using Donaldson’s holomorphic approximation method, we look forward to get the results which are similar to Demailly and Siu’s on almost complex manifold with local symplectic property or almost Kaehler manifold.