Equidistribution of minimal hypersurfaces for generic metrics

Abstract

For almost all Riemannian metrics (in the C∞ Baire sense) on a closed manifold Mⁿ⁺¹, 3 ≤ (n+1) ≤ 7, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3):963–972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich et al. (Ann Math 187(3):933–961, 2018).

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