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Published May 2019 | public
Journal Article

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).

Additional Information

The first author is partly supported by NSF-DMS-1509027 and NSF DMS-1311795. The second author is partly supported by NSF DMS-1710846 and EPSRC Programme Grant EP/K00865X/1. The third author is supported by NSF-DMS-1509027.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023