In this paper we prove that the tangent cones to calibrated 2cycles are unique. Furthermore, using this result we prove a rate of convergence for the mass of the blow-up of a calibrated integral 2-cycle C towards the limiting density: there exist constants C 1 > 0, γ > 0 such thatWe also obtain such a rate for J-holomorphic maps between almost complex manifolds and deduce that their tangent maps are unique.
We prove a regularity result for critical points of the polyharmonic energywith k ∈ N and p > 1. Our proof is based on a Gagliardo-Nirenberg-type estimate and avoids the moving frame technique. In view of the monotonicity formulae for stationary harmonic and biharmonic maps, we infer partial regularity in theses cases.
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