Lyusternik–Schnirelmann theory
GPTKB entity
Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:appliesTo |
smooth manifolds
|
| gptkbp:field |
gptkb:topology
critical point theory |
| gptkbp:hasConcept |
critical points of smooth functions
category of a topological space |
| https://www.w3.org/2000/01/rdf-schema#label |
Lyusternik–Schnirelmann theory
|
| gptkbp:influenced |
variational methods
critical point theory |
| gptkbp:introducedIn |
1930s
|
| gptkbp:namedAfter |
gptkb:Lazar_Lyusternik
gptkb:Lev_Schnirelmann |
| gptkbp:notableAchievement |
LS category provides lower bound for number of critical points
LS category of n-sphere is 2 every smooth function on a compact manifold has at least cat(M) critical points |
| gptkbp:relatedTo |
gptkb:topology
gptkb:Morse_theory |
| gptkbp:bfsParent |
gptkb:Lazar_Lyusternik
|
| gptkbp:bfsLayer |
7
|