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- Title
- Frankel's property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds
- KIAS Author
- Lee, Jaehoon
- Journal
- CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2025
- Archive
-
arXiv:2206.12581
- Abstract
- We study the behavior of minimal hypersurfaces in the Schwarzschild n-manifolds that intersect the horizon orthogonally along the boundary. We show that a free boundary minimal hypersurface and a totally geodesic hyperplane must intersect when the distance between them is achieved in a bounded region. We also discuss when the Schwarzschild metric is perturbed in a way that its scalar curvature is no longer positive.