VOLUMES OF PROJECTION BODIES OF SOME CLASSES OF CONVEX BODIES

DOI10.1112/S0025579311001860zbMath1267.52011MaRDI QIDQ3087008

Christos Saroglou

Publication date: 1 August 2011

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

coneszonotopesSteiner symmetrizationzonoidsdouble conesaffine invariant functional

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (3) dimensions (including convex surfaces) (52A15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (7)

Iterations of the projection body operator and a remark on Petty's conjectured projection inequality ⋮ Shadow systems: remarks and extensions ⋮ Fixed points of Minkowski valuations ⋮ On the equivalence between two problems of asymmetry on convex bodies ⋮ On inner and outer radii in Minkowski spaces ⋮ Minkowski symmetrization and projection bodies ⋮ On the shape of a convex body with respect to its second projection body

Cites Work

• On quermassintegrals of mixed projection bodies
• The difference body of a convex body
• Centroid surfaces
• Restricted chord projection and affine inequalities
• On isoperimetric inequalities in Minkowski spaces
• Zonoids with minimal volume-product
• The cross-section body, plane sections of convex bodies and approximation of convex bodies. I
• Kontinuierliche Linearkombination von Strecken
• Über die Projektionenkörper konvexer Polytope
• Volume in terms of concurrent cross-sections
• A new affine invariant for polytopes and Schneider’s projection problem
• Random polytopes and the volume-product of symmetric convex bodies.
• Random hyperplanes meeting a convex body
• Volumes of projection bodies
• Three-Dimensional Projection Bodies
• Extremal convex sets for Sylvester–Busemann type functionals

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