Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
gptkb:Laplace–Beltrami_operator
nodal sets of eigenfunctions |
| gptkbp:field |
gptkb:spectral_geometry
differential geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Yau's conjecture
|
| gptkbp:namedAfter |
gptkb:Shing-Tung_Yau
|
| gptkbp:provenBy |
gptkb:Donnelly_and_Fefferman
real analytic manifolds |
| gptkbp:provenYear |
1988
|
| gptkbp:relatedTo |
gptkb:Riemannian_manifolds
eigenvalues nodal hypersurfaces |
| gptkbp:requires |
the Hausdorff measure of the nodal set of the k-th eigenfunction is comparable to the square root of the eigenvalue
|
| gptkbp:statedIn |
1982
|
| gptkbp:status |
open (as of 2024)
|
| gptkbp:bfsParent |
gptkb:Shing-Chi_Yau
|
| gptkbp:bfsLayer |
5
|