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Rigidity of Complete Free Boundary Minimal Hypersurfaces in Convex NNSC Manifolds
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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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