Energy identity for approximations of harmonic maps from surfaces

Abstract

We prove the energy identity for min-max sequences of the Sacks-Uhlenbeck and the biharmonic approximation of harmonic maps from surfaces into general target manifolds. The proof relies on Hopf-differential type estimates for the two approximations and on estimates for the concentration radius of bubbles.

21 pages, statement of Theorem 1.1 corrected, to appear in Trans. Amer. Math. Soc