Existence of nontrival $n$-harmonic maps via min-max methods
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909985695334400 |
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| author | Martino, Dorian Mazowiecka, Katarzyna Schikorra, Armin |
| author_facet | Martino, Dorian Mazowiecka, Katarzyna Schikorra, Armin |
| contents | 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 $p \to n^+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of nontrival $n$-harmonic maps via min-max methods Martino, Dorian Mazowiecka, Katarzyna Schikorra, Armin Analysis of PDEs Differential Geometry 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 $p \to n^+$. |
| title | Existence of nontrival $n$-harmonic maps via min-max methods |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2601.05700 |