Bodies with similar projections

DOI10.1090/S0002-9947-97-01760-1zbMath0873.52010MaRDI QIDQ4336542

Erwin Lutwak, Gulbank D. Chakerian

Publication date: 13 May 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

mixed volumeconvex bodyzonoidquermassintegralAleksandrov's projection theoremgeneralized zonoidrelative brightnessrelative girth

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (16)

On polars of mixed projection bodies ⋮ An explicit counter-example for the Shephard problem of convex bodies in \(\mathbb R^n\) ⋮ Extremum of geometric functionals involving general \(L_{p}\)-projection bodies ⋮ General complex \(L_p\) projection bodies and complex \(L_p\) mixed projection bodies ⋮ Cross $i$-sections of star bodies and dual mixed volumes ⋮ The Petty projection inequality for \(L_p\)-mixed projection bodies ⋮ Projection problems for symmetric polytopes ⋮ Extremum problems for the cone volume functional of convex polytopes ⋮ Inequalities relating to \(L_p\) -version of petty's conjectured projection inequality ⋮ \(L_p\)-dual quermassintegral sums ⋮ Inequalities for polars of mixed projection bodies ⋮ Nakajima’s problem for general convex bodies ⋮ Smooth convex bodies with proportional projection functions ⋮ Even valuations on convex bodies ⋮ Extreme properties of quermassintegrals of convex bodies ⋮ On LYZ's conjecture for the \(U\)-functional

Cites Work

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• On the Aleksandrov-Fenchel inequality for convex bodies. I
• On the intermediate area functions of convex bodies
• Kontinuierliche Linearkombination von Strecken
• Über einige Eindeutigkeitssätze für konvexe Körper
• Centrally symmetric convex bodies and distributions. II
• Zu einem Problem von Shephard über die Projektionen konvexer Körper
• Über den Vektorraum der Differenzen von Stützfunktionen konvexer Körper
• Sets of Constant Relative Width and Constant Relative Brightness
• Convex bodies of constant outerp‐measure

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