Uniqueness of Tangent Cones to Positive-(p,p) Integral Cycles
  Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$, we get an almost hermitian manifold $(M, \om, J, g)$ and then $\Om$ is a so-called semi-calibration. We prove that integral cycles of dimension 2p (semi-)calibrated by $\Om$ possess at every point a unique tangent cone. The argument relies on an algebraic blow up perturbed in order to face the analysis issues of this problem in the almost complex setting. 
Costante Bellettini
math.AP math.DG