A Gap Theorem for the Möbius Cross Energy Near the Hopf Link

RESUMO

We prove that the critical value $2\pi^2$ is isolated for the Möbius cross energy of two-component links in the round three dimensional sphere $\mathbb{S}^{3}$. Specifically, there exists $\varepsilon_0>0$ such that any non-split, regular $H^2$ pair of curves with disjoint images, having vanishing first variation and energy at most $2\pi^2+\varepsilon_0$, must lie in the Möbius-reparametrization orbit of the standard Hopf link.