Energy identity for stationary biharmonic mappings into spheres in supercritical dimensions

Abstract

Energy identity for harmonic type maps in supercritical dimensions is an important and difficult problem. For sphere-valued harmonic maps, the first breakthrough was achieved by Lin-Rivière [Duke Math. J. 2002]. In this paper, by adapting their strategy, we establish the energy identity for stationary biharmonic maps into spheres in supercritical dimensions $n\ge 5$.

16 pages