Nonunique tangent maps at isolated singularities of minimizing $p$-harmonic maps

Abstract

The analysis of ``tangent maps'' at singular points of energy minimizing maps plays an important role in our understanding of the fine structure of the singular set. This note presents the first example of a minimizing (not just stationary) $p$-harmonic map with nonunique tangent maps at an isolated singularity. We construct a $n$-dimensional manifold $N$ such that for every admissible tuple $p< m\le n+2$, there exists a map from $B_1^m$ into $N$ that minimizes the $p$-energy, has an isolated singularity at the origin and admits a continuum of distinct tangent maps. The construction builds upon and extends B.~ White's example for $p=2$ in the stationary case.