Equidistribution of minimal hypersurfaces for generic metrics

Fernando Coda Maques Princeton University Andre Neves University of Chicago Antoine Song University of California, Berkeley

Differential Geometry mathscidoc:1909.10003

Inventiones Mathematicae, 2018
For almost all Riemannian metrics (in the C1 Baire sense) on a closed manifold M^{n+1}, 3 \leq n + 1 \leq 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 a result by Irie and the first two authors, that established density of minimal hypersurfaces for generic metrics. The main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich and the first two authors .
minimal hypersurfaces, equidistribution
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@inproceedings{fernando2018equidistribution,
  title={EQUIDISTRIBUTION OF MINIMAL HYPERSURFACES FOR GENERIC METRICS},
  author={Fernando Coda Maques, Andre Neves, and Antoine Song},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190929142421753703528},
  booktitle={Inventiones Mathematicae},
  year={2018},
}
Fernando Coda Maques, Andre Neves, and Antoine Song. EQUIDISTRIBUTION OF MINIMAL HYPERSURFACES FOR GENERIC METRICS. 2018. In Inventiones Mathematicae. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190929142421753703528.
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