Uniqueness of Tangent Cones to Positive-(p,p) Integral Cycles

Abstract

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.

22 pages

References in corpus (2)

• Semi-calibrated 2-currents are pseudo holomorphic, with applications
• Tangent cones to positive-(1,1) De Rham currents

Cited by in corpus (6)

• Uniqueness of tangent cones for $2$-dimensional almost minimizing currents
• Semi-calibrated 2-currents are pseudo holomorphic, with applications
• Non-unique conical and non-conical tangents to rectifiable stationary varifolds in R^4
• Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles
• The Unique Tangent Cone Property for Weakly Holomorphic Maps into Projective Algebraic Varieties
• Unique tangent behavior for 1-dimensional stationary varifolds