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Stable minimal hypersurfaces in $\mathbf{R}^5$

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arxiv 2401.01492 v3 pith:P22TGSU7 submitted 2024-01-03 math.DG

Otis Chodosh , Chao Li , Paul Minter , Douglas Stryker This is my paper · ORCID
classification math.DG
keywords mathbfminimalstablecompleteflathypersurfacehypersurfacestwo-sided
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abstract

We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat.

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Cited by 5 Pith papers

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

  1. Connected sum of manifolds with spectral Ricci lower bounds

    math.DG 2025-05 conditional novelty 7.0 of 10

    Connected sums preserve the spectral Ricci bound lambda1(-gamma Delta + Ric) > lambda for n >= 3 and gamma > (n-1)/(n-2), and this range is sharp.

  2. Spectral comparison results for the $N$-Bakry-Emery Ricci tensor

    math.DG 2024-12 conditional novelty 7.0 of 10

    The authors establish diameter and global weighted volume comparison theorems for manifolds with a positive spectral lower bound on the N-Bakry-Emery Ricci tensor.

  3. A sharp spectral splitting theorem

    math.DG 2024-12 conditional novelty 7.0 of 10

    If a complete noncompact n-manifold with at least two ends satisfies lambda1(-gamma Delta + Ric) >= 0 for some gamma < 4/(n-1), then it splits isometrically as R x N with compact N and Ric_N >= 0; the constant is sharp.

  4. 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.

  5. 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.

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