Existence of nontrival $n$-harmonic maps via min-max methods
Abstract
For any $n \geq 3$ and any closed manifold $\mathcal{N}$ with $π_{n+k}(\mathcal{N}) \neq \{0\}$ for some $k \geq 0$, we establish the existence of nontrivial $n$-harmonic maps from $\mathbb{S}^n$ into $\mathcal{N}$. When $k\geq 1$, these maps naturally appear as bubbling limits of $p$-harmonic maps with $p > n$, obtained by min-max constructions in the limit $p \to n^+$.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 January 2026
- Document type
- Preprint