PreprintCC BY 4.0arXiv
Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds
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 ∂ M. We then prove rigidity results of M in the corresponding equality cases.
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BibTeX
@misc{lee2026rigidity,
title = {{Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds}},
author = {Sanghun Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01392},
eprint = {2610.01392},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01392},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds
AU - Sanghun Lee
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01392
UR - https://arxiv.org/abs/2610.01392
AB - 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 ∂ M. We then prove rigidity results of M in the corresponding equality cases.
ER -