📝 SummarXiv

Abstract

We prove that the combination of strict positivity of $k$-tri-Ricci curvature with non-negative $3$-intermediate Ricci curvature forces rigidity of two-sided stable free boundary minimal hypersurface in a 5-manifold with bounded geometry and weakly convex boundary. This improves the result of Wu \cite{Wuyujie2023} to 5-dimensions and also extends the method of Hong-Yan \cite{Hong-cmc nonexis} to the free boundary case. We give a characterization of one-endedness for weakly stable free boundary constant mean curvature(FBCMC) hypersurfaces, which is an extension of Cheng-Cheung-Zhou \cite{Cheng-Cheung-Zhou2008}.