Time：9:00-10:30, Friday, September 12 2025
Tencent Meeting：898 3182 7279
Password: 541944
Host：Jintian Zhu, ITS
Speaker：Zetian Yan, UCSB
Title：Rigidity of CMC hypersurfaces in $5$- and $6$-manifolds
Language：中文
Abstract：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.
