Rigidity of CMC hypersurfaces in $5$- and $6$-manifolds

2025-09-05 16:42:03

时间:2025年9月12日(星期五),9:00-10:30

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主持人:Jintian Zhu, ITS

主讲人:Zetian Yan, UCSB

报告主题:Rigidity of CMC hypersurfaces in $5$- and $6$-manifolds

语言:中文

报告摘要:We prove that nonnegative $3$-intermediate Ricci curvature combined with uniformly positive $k$-triRic curvature implies rigidity of complete noncompact two-sided stable minimal hypersurfaces in a Riemannian manifold $(X^5,g)$ with bounded geometry. The stonger assumption of nonnegative $3$-intermediate Ricci curvature can be replaced by the nonnegativity of Ricci and biRic curvature. In particular, there is no complete noncompact stable minimal hypersurface in a closed $5$-dimensional manifold with positive sectional curvature. This extends result of Chodosh-Li-Stryker [J. Eur. Math. Soc (2025)] to $5$-dimension. We also establish rigidity results on CMC hypersurfaces with nonzero mean curvature in $5$- and $6$-manifolds.