Generic scarring for minimal hypersurfaces

In classical spectral theory, Equidistribution and Scarring concern the distribution of normalized energy measures for Laplacian eigenfunctions on closed manifolds. The Quantum Ergodicity asserts that in negative curvature a density one subsequence of Laplacian eigenfunctions has their normalized energy measures equidistributing, while Scarring means that some particular subsequence of normalized energy measures concentrate on proper subsets. In this talk, we will present a scarring phenomenon for minimal hypersurfaces for a generic set of smooth metrics. In particular, for generic metrics, to each stable hypersurface, there exists a sequence of minimal hypersurfaces, with area and Morse index both diverging to infinity, that accumulate along the stable hypersurface in a quantitative way. This is a joint work with Antoine Song.