We prove that every positive- integral cycle in an arbitrary almost-complex manifold possesses at every point a unique tangent cone. The argument relies on an algebraic blowup perturbed in order to face the analysis issues of this problem in the almost-complex setting.
Costante Bellettini. "Uniqueness of tangent cones to positive- integral cycles." Duke Math. J. 163 (4) 705 - 732, 15 March 2014. https://doi.org/10.1215/00127094-2429698