The structure and rigidiy of FBCMC hypersurfaces
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 Wuyujie2023 to 5-dimensions and also extends the method of Hong-Yan 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 Cheng-Cheung-Zhou2008.
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