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Gromov’s Weyl Law and Denseness of minimal hypersurfaces

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Gromov’s Weyl Law and Denseness of minimal hypersurfaces
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Minimal surfaces are ubiquitous in Geometry but they are quite hard to find. For instance, Yau in 1982 conjectured that any 3-manifold admitsinfinitely many closed minimal surfaces but the best one knows is the existence of at least two.In a different direction, Gromov conjectured a Weyl Law for the volume spectrum that was proven last year byLiokumovich, Marques, and myself. I will cover a bit the history of the problem and then talk about recent work with Irie, Marques, and myself: we combinedGromov’s Weyl Law with the Min-max theory Marques and I have been developing over the last years to prove that, for generic metrics, not only there are infinitely many minimal hypersurfaces but they are also dense.