Partial Regularity of Polyharmonic Maps to Targets of Sufficiently Simple Topology

Abstract

We prove that polyharmonic maps $\mathbb R^m \supset \Omega \to N$ locally minimizing $\int|D^kf|^2,dx$ are smooth on the interior of $\Omega$ outside a closed set $\Sigma$ with ${\mathcal H}^{m-2k}(\Sigma)=0$, provided that the target manifold $N \subset \mathbb R^n$ is smooth, closed, and fulfills $$ \pi\_1(N)=\ldots=\pi\_{2k-1}(N)=0. $$