On the ends of Willmore surfaces with curvature decay

Yuxiang Li; Hao Yin

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arXiv · 2606.01534

On the ends of Willmore surfaces with curvature decay

Yuxiang Li·Hao Yin

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Abstract

For a properly embedded Willmore surface $\Sigma$ in $\mathbb R^3$, we prove that if the scale-invariant second fundamental form is sufficiently small near infinity, the surface has finitely many ends. Moreover, if this scale-invariant quantity vanishes at infinity, or if there is only one end, the total $L^2$-norm of the second fundamental form is finite.

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Yuxiang Li, Hao Yin. 2026-06-01. On the ends of Willmore surfaces with curvature decay. https://arxiv.org/abs/2606.01534

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