Energy identity of approximate biharmonic maps to Riemannian manifolds and its application

Abstract

We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in Lp for p>43. We prove an energy identity that accounts for the loss of hessian energies by the sum of hessian energies over finitely many nontrivial biharmonic maps on R4. As a corollary, we obtain an energy identity for the heat flow of biharmonic maps at time infinity.