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Existence of minimal hypersurfaces with non-empty free Boundary for generic metrics
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 144, Number 2, April 2022
- pp. 599-606
- 10.1353/ajm.2022.0012
- Article
- Additional Information
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Abstract
abstract:
For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a compact manifold with boundary $(M^{n+1},\break\partial M)$, $3\leq (n+1)\leq 7$, we prove that, for any open subset $V$ of $\partial M$, there exists a compact, properly embedded free boundary minimal hypersurface intersecting $V$.
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