Energy identity for stationary biharmonic mappings into spheres in supercritical dimensions

TL;DR

This paper proves an energy identity for stationary biharmonic maps into spheres in supercritical dimensions, extending previous results for harmonic maps.

Contribution

It adapts existing strategies to establish energy identity for biharmonic maps into spheres in dimensions n ≥ 5.

Findings

Energy identity holds for stationary biharmonic maps in supercritical dimensions

Extension of techniques from harmonic to biharmonic maps

Applicable for dimensions n ≥ 5

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-Rivi\`ere [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 $n\ge 5$.