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arXiv · 2609.12102

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

Chuanhuan Li·Ronggang Li
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Abstract

We prove that the critical value $2π^2$ 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 $2π^2+\varepsilon_0$, must lie in the Möbius-reparametrization orbit of the standard Hopf link.

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Chuanhuan Li, Ronggang Li. 2026-09-15. A Gap Theorem for the Möbius Cross Energy Near the Hopf Link. https://arxiv.org/abs/2609.12102

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