Bubble classification of immersions at the boundary of the moduli space with $8π$ Willmore energy
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917388398624768 |
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| author | Scharrer, Christian Schlierf, Manuel West, Alexander |
| author_facet | Scharrer, Christian Schlierf, Manuel West, Alexander |
| contents | We study the asymptotic bubbling behavior of sequences of weak genus-$p$ immersions with diverging conformal classes and limiting Willmore energy of $8π$. After applying suitable Möbius transformations, in a strong $W^{2,2}_{\mathrm{loc}}$-limit, we obtain two round spheres at the largest scale and $p+1$ catenoids at the smallest scales. Moreover, we apply this classification to sequences of isoperimetrically, conformally and normalized-total-mean-curvature constrained Willmore minimizers when the constraints approach the boundary of the domain where minimizers exist, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bubble classification of immersions at the boundary of the moduli space with $8π$ Willmore energy Scharrer, Christian Schlierf, Manuel West, Alexander Differential Geometry 53C42, 53A30, 49Q10 We study the asymptotic bubbling behavior of sequences of weak genus-$p$ immersions with diverging conformal classes and limiting Willmore energy of $8π$. After applying suitable Möbius transformations, in a strong $W^{2,2}_{\mathrm{loc}}$-limit, we obtain two round spheres at the largest scale and $p+1$ catenoids at the smallest scales. Moreover, we apply this classification to sequences of isoperimetrically, conformally and normalized-total-mean-curvature constrained Willmore minimizers when the constraints approach the boundary of the domain where minimizers exist, respectively. |
| title | Bubble classification of immersions at the boundary of the moduli space with $8π$ Willmore energy |
| topic | Differential Geometry 53C42, 53A30, 49Q10 |
| url | https://arxiv.org/abs/2604.05932 |