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Complete stable minimal hypersurfaces in positively curved 4-manifolds

  • Otis Chodosh

    Stanford University, Stanford, USA

  • Chao Li

    New York University, New York, USA

  • Douglas Stryker

    Princeton University, Princeton, USA
Complete stable minimal hypersurfaces in positively curved 4-manifolds cover

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Abstract

We show that the combination of non-negative sectional curvature (or -intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) two-sided stable minimal hypersurfaces in a -manifold with bounded curvature. Our work leads to new comparison results. We also construct various examples showing that rigidity of stable minimal hypersurfaces can fail under other curvature conditions.

Cite this article

Otis Chodosh, Chao Li, Douglas Stryker, Complete stable minimal hypersurfaces in positively curved 4-manifolds. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1499