Full generic regularity II for min-max minimal hypersurfaces

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Let Mn+1M^{n+1} be a closed smooth manifold, and let gg be a Baire C∞C^\infty-generic Riemannian metric on MM. A min-max gg-minimal hypersurface is a minimal hypersurface generated by min-max theory. Full generic regularity II. Every min-max gg-minimal hypersurface is smooth. This extends the preceding generic regularity conjecture from area minimizers to min-max minimal hypersurfaces, which are not generally area minimizing. The conjecture is relevant to extending generic regularity and density results to higher dimensions.

References

Primary source

Yangyang Li and Zhihan Wang, “Minimal hypersurfaces for generic metrics in dimension 8”, arXiv:2205.01047 (2022).

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