Convex and discrete geometry Convex sets: basic notions Concept
Convex body
Summary
A convex body is a compact convex set in with nonempty interior. Convex bodies are the main objects of convex geometry: balls, cubes, simplices and all convex polytopes of full dimension are examples. Volume, surface area, mixed volumes and the Brunn–Minkowski theory are all developed for convex bodies.
Where this leads
22 pages build on this one.
- Quermassintegral
- Steiner symmetrization
- Zonoid
- Minkowski's first inequality
- Mixed volume
- Alexandrov–Fenchel inequality
- John ellipsoid
- Steiner formula
- Curve of constant width
- Mahler conjecture
- Illumination problem
- Danzer set
- Blaschke–Santaló inequality
- Busemann–Petty problem
- Minkowski problem
- Intrinsic volume
- Projection body
- Valuation on convex bodies
- Intersection body
- Hadwiger covering conjecture
- Löwner–John theorem
- Brunn–Minkowski theory
Further reading
About this page
| Tag | 437FSG3419 |
|---|---|
| URI | m2://437FSG3419 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 52A20 |
| Specializes | Convex set |
| Same as |
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Used by
- Quermassintegral
- Steiner symmetrization
- Zonoid
- Minkowski's first inequality
- Mixed volume
- Alexandrov–Fenchel inequality
- John ellipsoid
- Steiner formula
- Curve of constant width
- Mahler conjecture
- Illumination problem
- Danzer set
- Blaschke–Santaló inequality
- Busemann–Petty problem
- Minkowski problem
- Intrinsic volume
- Projection body
- Valuation on convex bodies
- Intersection body
- Hadwiger covering conjecture
- Löwner–John theorem
- Brunn–Minkowski theory
Results about this
- Mahler conjecture
- Illumination problem
- Danzer set
- Blaschke–Santaló inequality
- Busemann–Petty problem
- Minkowski problem
- Hadwiger covering conjecture