Equidistribution of minimal hypersurfaces for generic metrics

Abstract

For almost all Riemannian metrics (in the $C^{\infty }$ Baire sense) on a closed manifold $M^{n+1}$, $3\le (n+1)\le 7$, 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 \cite{irie-marques-neves}, by Irie and the first two authors, that established denseness of minimal hypersurfaces for generic metrics. As in \cite{irie-marques-neves}, the main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich and the first two authors in \cite{liokumovich-marques-neves}.

References have been added. Final version to appear in Inventiones Mathematicae

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