Existence of nontrival n-harmonic maps via min-max methods.

Abstract

For any $n\ge 3$ and any closed manifold $N$ with ${\pi }_{n+k}\left(N\right)\ne \left\{0\right\}$ for some $k\ge 0$ , we establish the existence of nontrivial n-harmonic maps from $S^n$ into $N$ . When $k\ge 1$ , these maps naturally appear as bubbling limits of p-harmonic maps with $p>n$ , obtained by min-max constructions in the limit $p\to n^{+}$ .