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arXiv · 2606.15644

Minimizing and non-minimizing degree one $W^{s,1/s}$-harmonic maps between spheres

Dorian Martino·Katarzyna Mazowiecka·Armin Schikorra
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Abstract

We show that $id:\mathbb{S}^1 \to \mathbb{S}^1$ is \emph{not} a minimizing $W^{s,\frac{1}{s}}$-harmonic map for $s \in (0,\frac{1}{8}$). On the other hand, for $s \in (\frac{1}{3},1)$ it is a local minimizing map, and for $s\in [\frac{1}{2}-\varepsilon,\frac{1}{2}+\varepsilon]$ it is a global minimizer. The usual extension or Fourier techniques being unavailable, our argument relies instead of stability analysis in $s$.

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Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra. 2026-06-14. Minimizing and non-minimizing degree one $W^{s,1/s}$-harmonic maps between spheres. https://arxiv.org/abs/2606.15644

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