Density of minimal hypersurfaces for generic metricsc

Kei Irie; Fernando C. Marques; André Neves

doi:10.4007/annals.2018.187.3.8

Density of minimal hypersurfaces for generic metricsc

Kei Irie, Fernando C. Marques, André Neves

Mathematics

Research output: Contribution to journal › Article › peer-review

78 Scopus citations

Abstract

For almost all Riemannian metrics (in the C^∞ Baire sense) on a closed manifold Mⁿ⁺¹, 3 ≤ (n + 1) ≤ 7, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces, thus proving a conjecture of Yau (1982) for generic metrics.

Original language	English (US)
Pages (from-to)	963-972
Number of pages	10
Journal	Annals of Mathematics
Volume	187
Issue number	3
DOIs	https://doi.org/10.4007/annals.2018.187.3.8
State	Published - May 1 2018

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Generic metrics
Minimal surfaces
Weyl law

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10.4007/annals.2018.187.3.8

Cite this

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AU - Neves, André

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N2 - For almost all Riemannian metrics (in the C∞ Baire sense) on a closed manifold Mn+1, 3 ≤ (n + 1) ≤ 7, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces, thus proving a conjecture of Yau (1982) for generic metrics.

AB - For almost all Riemannian metrics (in the C∞ Baire sense) on a closed manifold Mn+1, 3 ≤ (n + 1) ≤ 7, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces, thus proving a conjecture of Yau (1982) for generic metrics.

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KW - Minimal surfaces

KW - Weyl law

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Density of minimal hypersurfaces for generic metricsc

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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