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arXiv · 2601.18388

Stability of the free boundary Willmore problem

Anna Dall'Acqua·Fabian Rupp·Reiner Schätzle·Manuel Schlierf
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Abstract

We study the Willmore problem with free boundary by means of a new {\L}ojasiewicz-Simon gradient inequality for functionals on infinite dimensional manifolds. In contrast to previous works, we do not rely on a gradient-like representation of the Fr\'echet derivative, but merely on an inequality. For the free boundary Willmore flow, we prove that solutions starting sufficiently close to a local minimizer exist for all times and converge. In the static setting, we prove quantitative stability of free boundary Willmore immersions and a local rigidity result in a neighborhood of free boundary minimal surfaces.

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Anna Dall'Acqua, Fabian Rupp, Reiner Schätzle, Manuel Schlierf. 2026-01-26. Stability of the free boundary Willmore problem. https://arxiv.org/abs/2601.18388

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