Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
2-dimensional tori
|
| gptkbp:field |
gptkb:Riemannian_geometry
differential geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Loewner's inequality
|
| gptkbp:namedAfter |
gptkb:Charles_Loewner
|
| gptkbp:relatedTo |
gptkb:systole
systolic geometry isoperimetric inequality |
| gptkbp:sentence |
For any Riemannian metric on the 2-torus, the square of the length of the shortest non-contractible loop is at most (2/√3) times the area of the torus.
|
| gptkbp:yearProposed |
1949
|
| gptkbp:bfsParent |
gptkb:Loewner's_torus_inequality
|
| gptkbp:bfsLayer |
7
|