PreprintCC BY 4.0arXiv
A Gap Theorem for the Möbius Cross Energy Near the Hopf Link
Abstract
We prove that the critical value 2π2 is isolated for the Möbius cross energy of two-component links in the round three dimensional sphere 𝕊3. Specifically, there exists ε0>0 such that any non-split, regular H2 pair of curves with disjoint images, having vanishing first variation and energy at most 2π2+ε0, must lie in the Möbius-reparametrization orbit of the standard Hopf link.
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BibTeX
@misc{li2026theorem,
title = {{A Gap Theorem for the Möbius Cross Energy Near the Hopf Link}},
author = {Chuanhuan Li and Ronggang Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12102},
eprint = {2609.12102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12102},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Gap Theorem for the Möbius Cross Energy Near the Hopf Link
AU - Chuanhuan Li
AU - Ronggang Li
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.12102
UR - https://arxiv.org/abs/2609.12102
AB - 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 𝕊^3. Specifically, there exists ε_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+ε_0, must lie in the Möbius-reparametrization orbit of the standard Hopf link.
ER -