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arXiv · 2610.01392

Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds

Sanghun Lee
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Abstract

In this paper, we establish a volume estimate and an associated rigidity result for volume-minimizing free boundary hypersurfaces in an $(n+1)$-dimensional Riemannian manifold $M$. First, we derive a volume estimate for stable minimal free boundary hypersurfaces in terms of the scalar curvature of $M$ and the second fundamental form of the boundary $\partial M$. We then prove rigidity results of $M$ in the corresponding equality cases.

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Sanghun Lee. 2026-10-01. Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds. https://arxiv.org/abs/2610.01392

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