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We show that the combination of non-negative sectional curvature (or 2 -intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) two-sided stable minimal hypersurfaces in a 4 -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.
Chodosh et al. (Fri,) studied this question.