Energy identity for intrinsically biharmonic maps in four dimensions

Let u be a mapping from a bounded domain S ⊂ ℝ4 into a compact Riemannian manifold N. Its intrinsic biharmonic energy E2.u/ is given by the squared L2-norm of the intrinsic Hessian of u. We consider weakly converging sequences of critical points of E2. Our main result is that the energy dissipation along such a sequence is fully due to energy concentration on a finite set and that the dissipated energy equals a sum over the energies of finitely many entire critical points of E1.