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Stable minimal hypersurfaces in $\mathbb R^6$

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arxiv 2405.14676 v1 pith:T5ALRWX2 submitted 2024-05-23 math.DG

Laurent Mazet This is my paper · ORCID
classification math.DG
keywords hypersurfacesmathbbminimalstableantonellichodoshcompletedeveloped
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abstract

Following the strategy developed by Chodosh, Li, Minter and Stryker, and using the volume estimate of Antonelli and Xu, we prove that, in $\mathbb R^6$, a complete, two-sided, stable minimal hypersurfaces is flat.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Minimal hypersurfaces of Morse index one

    math.DG 2026-07 accept novelty 7.0 of 10

    Any complete connected embedded minimal hypersurface in R^{n+1} with finite total curvature and Morse index one is a higher-dimensional catenoid.

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  3. Some rigidity theorems for spectral curvature bounds

    math.DG 2026-04 accept novelty 6.5 of 10

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  4. Area-charge inequalities and rigidity of time-symmetric initial data sets

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    In charged Einstein-Maxwell initial data sets, a boundary surface must have area at least a sharp function of its electric charge and the cosmological constant, with equality only for product geometries.

  5. Complete two-sided $\delta$-stable minimal hypersurfaces in $\mathbf R^{n+1}$

    math.DG 2025-07 conditional novelty 6.0 of 10

    For n=3,4,5 and δ above thresholds δ0(n), complete two-sided δ-stable minimal hypersurfaces in R^{n+1} have Euclidean volume growth, and for δ above δ1(n) they are hyperplanes.

  6. Stable anisotropic minimal hypersurfaces in $\mathbb{R}^{5}$ and $\mathbb{R}^{6}$

    math.DG 2025-05 conditional novelty 6.0 of 10

    Complete stable anisotropic minimal hypersurfaces in R^5 and R^6 are flat whenever the anisotropic area functional is C^4-close to the standard area functional.

  7. Isoperimetric problems and lower bounds on curvature

    math.DG 2025-09 conditional novelty 2.0 of 10

    Survey of isoperimetric problems under lower Ricci curvature bounds, presenting sharp concavity inequalities, recent existence results, and open questions.

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