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

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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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.