Uniqueness and Regularity of the Fractional Harmonic Gradient Flow in $S^{n-1}$

Abstract

In this paper, we study the fractional harmonic gradient flow on $S^1$ taking values in $S^{n-1}\subset {\mathbb{R}}^n$ for every $n\ge 2$, in particular addressing uniqueness and regularity of solutions in the so-called energy class with sufficiently small energy, adding to the existing body of knowledge which includes existence of solutions and certain bubbling phenomena.

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• n/p-Harmonic maps: regularity for the sphere case
• On regularity theory for n/p-harmonic maps into manifolds
• Free boundary minimal surfaces: a nonlocal approach
• Infinite time blow-up for half-harmonic map flow from $\mathbb{R}$ into ${\mathbb{S}}^1$
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Cited by in corpus (2)

• Non-degeneracy and quantitative stability of half-harmonic maps from $\mathbb{R}$ to $\mathbb{S}$
• Plateau flow or the heat flow for half-harmonic maps