Existence of minimal hypersurfaces with non-empty free boundary for generic 
metrics

Wang, Zhichao

doi:10.1353/ajm.2022.0012

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Existence of minimal hypersurfaces with non-empty free boundary for generic metrics

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Wang, Zhichao
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1353/ajm.2022.0012
(Publisher version)

https://doi.org/10.48550/arXiv.1909.01787
(Preprint)

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Citation

Wang, Z. (2022). Existence of minimal hypersurfaces with non-empty free boundary for generic metrics. American Journal of Mathematics, 14(2), 599-606. doi:10.1353/ajm.2022.0012.

Cite as: https://hdl.handle.net/21.11116/0000-000A-22A0-A

Abstract

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a
compact manifold with boundary $(M^{n+1},\partial M)$, $3\leq (n + 1)\leq 7$,
we prove that, for any open subset $V$ of $\partial M$, there exists a compact,
properly embedded free boundary minimal hypersurface intersecting $V$.