Georgia Institute of Technology College of Sciences

For a map u from a Riemann surface M to a Riemannian manifold and a>1, the a-energy functional is defined as E_a(u)=\int_M |\nabla u|^{2a}dx. We call u_a a sequence of Sacks-Uhlenbeck maps if u_a is a critical point of E_a, and sup_{a>1} E_a(u_a)<\infty. In this talk, when the target manifold is a standard sphere S^K, we prove the energy identity for a sequence of Sacks-Uhlenbeck maps during blowing up.