Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Riemannian_manifolds
|
| gptkbp:concerns |
Ricci curvature
volume comparison |
| gptkbp:field |
gptkb:Riemannian_geometry
|
| gptkbp:namedAfter |
gptkb:Mikhail_Gromov
gptkb:Richard_L._Bishop |
| gptkbp:publishedIn |
gptkb:Bishop,_R._L.;_Crittenden,_R._J._(1964)._Geometry_of_Manifolds.
gptkb:Gromov,_M._(1981)._Structures_métriques_pour_les_variétés_riemanniennes. |
| gptkbp:state |
The ratio of the volume of a metric ball to the volume of a ball in a model space of constant curvature is non-increasing as the radius increases, under Ricci curvature lower bound.
|
| gptkbp:usedIn |
global analysis
comparison geometry |
| gptkbp:bfsParent |
gptkb:Comparison_geometry
|
| gptkbp:bfsLayer |
7
|
| http://www.w3.org/2000/01/rdf-schema#label |
Bishop–Gromov inequality
|