Density of minimal hypersurfaces for generic metricsc

Kei Irie, Fernando C. Marques, André Neves

Research output: Contribution to journalArticle

11 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 languageEnglish (US)
Pages (from-to)963-972
Number of pages10
JournalAnnals of Mathematics
Volume187
Issue number3
DOIs
StatePublished - 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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