A rigidity estimate for maps from $S^2$ to $S^2$ via the harmonic map flow

Abstract

We show how a rigidity estimate introduced in recent work of Bernand-Mantel, Muratov and Simon can be derived using the harmonic map flow.

References in corpus (1)

• A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree $\pm 1$ harmonic maps from ${\mathbb{R}}^2$ to ${\mathbb{S}}^2$

Cited by in corpus (2)

• Rigidity estimates for isometric and conformal maps from ${\mathbb{S}}^{n-1}$ to ${\mathbb{R}}^n$
• Non-degeneracy and quantitative stability of half-harmonic maps from $\mathbb{R}$ to $\mathbb{S}$