论文标题
在正面弯曲的4个manifolds中，完全稳定的最小曲面
Complete stable minimal hypersurfaces in positively curved 4-manifolds
论文作者
论文摘要
我们表明，非负分段曲率（或$ 2 $互助曲率）与完全（非压缩的）两侧稳定稳定的最小超出性的标量曲率刚度的严格阳性在$ 4 $ - manifold culvatator中。特别是，这意味着在封闭的$ 4 $ manifold中，完全双面稳定的最小超出表面不存在，截面曲率为正。 我们的工作带来了新的比较结果。我们还构建了各种示例，显示稳定的最小超曲面的刚性在其他曲率条件下可能会失败。
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. In particular, this implies the nonexistence of complete two-sided stable minimal hypersurface in a closed $4$-manifold with positive sectional curvature. Our work leads to new comparison results. We also construct various examples showing rigidity of stable minimal hypersurfaces can fail under other curvature conditions.
