Minimal hypersurfaces for generic metrics in dimension 8
Abstract
We show that in an 8-dimensional closed Riemmanian manifold with C∞-generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic regularity conjecture of minimal hypersurfaces in dimension eight. This also enables us to generalize many generic geometric properties of (Almgren-Pitts) min-max minimal hypersurfaces, previously only known in low dimensions, to dimension eight.
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