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arXiv · 2504.20585

Rigidity of Complete Free Boundary Minimal Hypersurfaces in Convex NNSC Manifolds

Yujie Wu
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Abstract

We prove that in the unit ball of $\mathbb{R}^4$, there is no complete two-sided stable free boundary immersion. The result follows from a rigidity theorem of complete free boundary minimal hypersurfaces in complete 4-manifolds with non-negative intermediate Ricci curvature, convex boundary and weakly bounded geometry. The method uses warped $\theta$-bubble, a generalization of capillary surfaces.

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Yujie Wu. 2025-04-29. Rigidity of Complete Free Boundary Minimal Hypersurfaces in Convex NNSC Manifolds. https://arxiv.org/abs/2504.20585

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