Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Lee, Sanghun
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215736523