Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
convex bodies
compact subsets of Euclidean space |
| gptkbp:field |
gptkb:geometry
gptkb:mathematics convex geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Brunn–Minkowski theorem
|
| gptkbp:implies |
gptkb:Minkowski_inequality
isoperimetric inequality |
| gptkbp:namedAfter |
gptkb:Hermann_Minkowski
Hermann Brunn |
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Minkowski_sum
|
| gptkbp:sentence |
The n-th root of the volume of the Minkowski sum of two non-empty compact subsets of n-dimensional Euclidean space is at least the sum of the n-th roots of the volumes of the two sets.
|
| gptkbp:usedIn |
gptkb:information_theory
gptkb:probability_theory analysis |
| gptkbp:yearProposed |
1887
|
| gptkbp:bfsParent |
gptkb:Convex_geometry
|
| gptkbp:bfsLayer |
7
|