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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Generic metrics
- Minimal surfaces
- Weyl law