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

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000A-22A0-A Version Permalink: https://hdl.handle.net/21.11116/0000-000A-22A1-9
Genre: Journal Article

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1909.01787.pdf (Preprint), 150KB
 
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 Creators:
Wang, Zhichao1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Differential Geometry, Analysis of PDEs, Geometric Topology
 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 $V$.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 1909.01787
DOI: 10.1353/ajm.2022.0012
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Title: American Journal of Mathematics
Source Genre: Journal
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Publ. Info: Johns Hopkins University Press
Pages: - Volume / Issue: 14 (2) Sequence Number: - Start / End Page: 599 - 606 Identifier: -