Costante Bellettini

Almost complex structures and calibrated integral cycles in contact 5-manifolds

Abstract. In a contact manifold , we consider almost complex structures J that satisfy, for any vector v in the horizontal distribution, . We prove that two-dimensional integral cycles whose approximate tangent planes have the property of being J-invariant and positively oriented are in fact smooth Legendrian curves except possibly at isolated points and we investigate how such structures J are related to calibrations.

Uniqueness of tangent cones to positive-(p,p) integral cycles

Let

Semi-calibrated 2-currents are pseudoholomorphic, with applications

(M, \om)

Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles

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

The regularity of Special Legendrian Integral Cycles

\Om := \frac{\om^p}{p!}

Tangent cones to positive-(1,1) De Rham currents

is a calibration. More generally, dropping the closedness assumption on

Regularity of sets with constant horizontal normal in the Engel group

\om

Compactness results for triholomorphic maps

, we get an almost hermitian manifold

Stable CMC integral varifolds of codimension

(M, \om, J, g)

1

and then