On conservation laws for polyharmonic maps

Abstract

This article provides an overview on various conservation laws for polyharmonic maps between Riemannian manifolds. Besides recalling that the variation of the energy for polyharmonic maps with respect to the domain metric gives rise to the stress-energy tensor, we also show how the presence of a Killing vector field on the target manifold leads to a conservation law. For harmonic and biharmonic maps we also point out a number of applications of such conservation laws.