The Singular Set of Stable Minimal Hypersurfaces

Explore a 49-minute conference talk by Leon Simon at BIMSA on the singular set of stable minimal hypersurfaces. Delve into the history of singularities in stable embedded minimal hypersurfaces, starting with the 1981 work of Richard Schoen and the speaker. Learn about the absence of singularities in dimensions 6 and below, and the existence of singularities forming a closed set of dimension at most n-7 for dimensions 7 and above. Discover the speaker's recent work demonstrating that for any closed subset K of a specific form in higher dimensions, there exists a smooth Riemannian metric on the ambient space that admits stable embedded minimal hypersurfaces with singular set exactly equal to K. Gain insights into this advanced topic in geometric analysis and its implications for understanding the structure of minimal surfaces in higher dimensions.