# Generic Regularity of Minimal Hypersurfaces in Dimension 8.

@article{Li2020GenericRO, title={Generic Regularity of Minimal Hypersurfaces in Dimension 8.}, author={Yangyang Li and Zhihan Wang}, journal={arXiv: Differential Geometry}, year={2020} }

In this paper, we show that every $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics admits a smooth minimal hypersurface.

## 5 Citations

### Minimal hypersurfaces for generic metrics in dimension 8

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- 2022

. 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…

### Mean Convex Smoothing of Mean Convex Cones

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We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a…

### Singular behavior and generic regularity of min-max minimal hypersurfaces

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We show that for a generic $8$-dimensional Riemannian manifold with positive Ricci curvature, there exists a smooth minimal hypersurface. Without the curvature condition, we show that for a dense set…

### SOME NEW GENERIC REGULARITY RESULTS FOR MINIMAL SURFACES AND MEAN CURVATURE FLOWS LECTURE NOTES FOR GEOMETRIC ANALYSIS FESTIVAL, 2021

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For Γn−1 ⊂ ∂B1 ⊂ R, consider Σ ⊂ B1 a hypersurface with ∂Σ = Γ, with least area among all such surface. (This is known as the Plateau problem). It might happen that Σ is singular. For example,…

### Mean curvature flow with generic low-entropy initial data

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. We prove that suﬃciently low-entropy closed hypersurfaces can be perturbed so that their mean curvature ﬂow encounters only spherical and cylindrical singularities. Our theorem applies to all…

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