Regularity of minimizing harmonic maps into \(S^ 4\), \(S^ 5\) and symmetric spaces
We prove that for \(n=4\), 5 every energy minimizing map from a manifold \(M\) of dimension \(n\) into the Euclidean sphere \(S^ n\) is regular in the interior of \(M\). This improves a result of R. Schoen and K. Uhlenbeck. We also prove a Liouville type theorem for smooth stable harmonic maps from noncompact complete Riemannian manifolds with nonnegative Ricci curvature into \(S^ n\).
scientific article; zbMATH DE number 537316
scientific article