Elastic curves and Willmore Hopf-Tori
Elastic curves and Willmore Hopf-Tori
Elastic curves and Willmore Hopf-Tori
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TheoremThe <strong>Willmore</strong> energy along each deformation family containing a<strong>Willmore</strong> <strong>Hopf</strong>-torus attains its maximum at this torus. The2-lobed <strong>Willmore</strong> <strong>Hopf</strong>-torus has the least energy among the<strong>Willmore</strong> <strong>Hopf</strong>-tori.Figure:The 2-lobed <strong>Willmore</strong> torus, <strong>and</strong> its free elastic profile curve.