Reduced convex bodies in Euclidean space -- a survey
DOI10.1016/j.exmath.2011.01.006zbMath1213.52006OpenAlexW1974783611MaRDI QIDQ534169
Publication date: 17 May 2011
Published in: Expositiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.exmath.2011.01.006
thicknessdiameterconvex bodyconstant widthperimetercomplete setminimal widthisodiametric problemreduced bodywidth function
Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Isoperimetric problems for polytopes (52B60) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (17)
Cites Work
- Estimates for the minimal width of polytopes inscribed in convex bodies
- Reduced bodies in Minkowski space
- Characterizations of reduced polytopes in finite-dimensional normed spaces
- Reduced convex bodies in the plane
- Isoperimetric polygons of maximum width
- On pyramids and reducedness
- Extremal convex sets
- Konvexe Bereiche kleinster Oberfläche bei gegebener Dicke. (Convex domains of given thickness with smallest surface area)
- Reduced strictly convex plane figure is of constant width
- On complete convex bodies
- Das Volumen spezieller konvexer Polytope. (On the volume of special convex polytopes)
- Konstruktion regulärer Hüllen konstanter Breite
- Inner and outer \(j\)-radii of convex bodies in finite-dimensional normed spaces
- Unsolved problems in geometry
- On the smallest disk containing a planar reduced convex body
- On planar convex bodies of given Minkowskian thickness and least possible area
- On reduced convex bodies
- Tetrahedra are not reduced
- Lower bounds for volumes of convex bodies
- Reduced bodies in normed planes
- The geometry of Minkowski spaces -- a survey. II.
- Characterizations of central symmetry for convex bodies in Minkowski spaces
- The Shortest Planar Arc of Width 1
- On the Inequality for Volume and Minkowskian Thickness
- On reduced polytopes and antipodality
- The volume of certain convex sets
- Bodies of constant width in arbitrary dimension
- On the Size of Equilateral Triangles Which May Be Inscribed in Curves of Constant Width
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