On the ends of Willmore surfaces with curvature decay
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913177922437120 |
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| author | Li, Yuxiang Yin, Hao |
| author_facet | Li, Yuxiang Yin, Hao |
| contents | For a properly embedded Willmore surface $Σ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01534 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the ends of Willmore surfaces with curvature decay Li, Yuxiang Yin, Hao Differential Geometry Analysis of PDEs For a properly embedded Willmore surface $Σ$ 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. |
| title | On the ends of Willmore surfaces with curvature decay |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2606.01534 |