• Corpus ID: 232352577

Degeneration of 7-dimensional minimal hypersurfaces which are stable or have bounded index

@inproceedings{Edelen2021DegenerationO7,
title={Degeneration of 7-dimensional minimal hypersurfaces which are stable or have bounded index},
author={Nick Edelen},
year={2021}
}
A 7-dimensional area-minimizing embedded hypersurface $M$ will in general have a discrete singular set. The same is true if $M$ is stable, or has bounded index, provided $H^6(sing M) = 0$. We show that if $M_i$ are a sequence of such minimal hypersurfaces which are minimizing, stable, or have bounded index, then $M_i$ can limit to a singular $M$ with only very controlled geometry, topology, and singular set. We show one can always"parameterize"a subsequence $i'$ with controlled bi-Lipschitz…
3 Citations

Minimal hypersurfaces for generic metrics in dimension 8

• Mathematics
• 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

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

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,

Generic Regularity of Minimal Hypersurfaces in Dimension 8.

• Mathematics
• 2020
In this paper, we show that every $8$-dimensional closed Riemmanian manifold with $C^\infty$-generic metrics admits a smooth minimal hypersurface.