Mathematics > Differential Geometry
arXiv:2606.01534 (math)
[Submitted on 1 Jun 2026]
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.
Submission history
From: Hao Yin [view email]
[v1]
Mon, 1 Jun 2026 01:32:11 UTC (26 KB)
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