Singular points of harmonic maps from 4-dimensional domains into 3-spheres (Q2496425)

This paper has two main results: 1) Let \(\Omega \) be a bounded domain in \(\mathbb R^4\) and \(u:\Omega \rightarrow S^{3}\) a stable-stationary harmonic map. Then the mapping degree of \(u\) at a singular point is \(\pm 1\). 2) Any non-constant stable-stationary tangent map from the ball \(B^{4}\) to \(S^{3}\) is a homogeneous extension of an isometry of \(S^{3}\).