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arXiv · 2604.05932

Bubble classification of immersions at the boundary of the moduli space with $8\pi$ Willmore energy

Christian Scharrer·Manuel Schlierf·Alexander West
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Abstract

We study the asymptotic bubbling behavior of sequences of weak genus-$p$ immersions with diverging conformal classes and limiting Willmore energy of $8\pi$. After applying suitable M\"obius 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.

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Christian Scharrer, Manuel Schlierf, Alexander West. 2026-04-07. Bubble classification of immersions at the boundary of the moduli space with $8\pi$ Willmore energy. https://arxiv.org/abs/2604.05932

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