On the bumpy metrics theorem for minimal submanifolds
By B. White. 2015
89 citations recorded by the source corpus.
This paper proves several natural generalizations of the theorem that for a generic, $C^k$ Riemannian metric on a smooth manifold, there are no closed, embedded, minimal submanifolds with nontrivial Jacobi fields.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/722663336add169361d19241a036538d46dac86a
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Morse index of multiplicity one min-max minimal hypersurfaces (2015, background): “White showed in [57, 59] that bumpy metrics are generic in the usual C∞ Baire sense.”
- Minimal 2-spheres in 3-spheres (2017, background): “This is a generic property for metrics [34].”
- On the Multiplicity One Conjecture in min-max theory (2019, unknown): “White proved that the set of bumpy metrics is generic in the Baire sense [42, 44].”
- Compactness analysis for free boundary minimal hypersurfaces (2017, methodology): “ite covers of any such hypersurface, admit a non-trivial Jacobi field. Then Bq is a comeagre subset of Γq. This is the free boundary counterpart of Theorem 2.2 in [41] (for finite q) and Theorem 2.1 in [44] (for q= ∞). The definition of comeagre set and an appropriate contextualization of this result a”
- Density of minimal hypersurfaces for generic metrics. (2017, methodology): “By the Bumpy Metrics Theorem of White (Theorem 2.1 in [18]), there exists g (cid:48) ∈ V such that every closed, smooth immersed minimal hypersurface with respect to g (cid:48) is nondegenerate.”