Some inequalities about mixed volumes

DOI10.1007/BF02776055zbMath1045.52002MaRDI QIDQ1424034

Apostolos Giannopoulos, Mathieu Meyer, Matthieu Fradelizi

Publication date: 8 March 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

projectionsquermassintegralsmixed volumesBergstrom's inequalityMinkowski's sums

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (18)

On a local version of the Aleksandrov-Fenchel inequality for the quermassintegrals of a convex body ⋮ On the quermassintegrals of convex bodies ⋮ Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies ⋮ Convergence of symmetrization processes ⋮ On inner parallel bodies and quermassintegrals ⋮ Extremizers in Soprunov and Zvavitch's Bezout inequalities for mixed volumes ⋮ Weighted Brunn-Minkowski theory. I: On weighted surface area measures ⋮ On the analogue of the concavity of entropy power in the Brunn-Minkowski theory ⋮ Volumes of subset Minkowski sums and the Lyusternik region ⋮ Short note on some geometric inequalities derived from matrix inequalities ⋮ On the volume of the Minkowski sum of zonoids ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ On isoperimetric inequality in Arakelov geometry ⋮ Differentiability of quermassintegrals: A classification of convex bodies ⋮ The convexification effect of Minkowski summation ⋮ REMARKS ABOUT MIXED DISCRIMINANTS AND VOLUMES ⋮ Rogers-Shephard and local Loomis-Whitney type inequalities ⋮ Wulff shapes and a characterization of simplices via a Bezout type inequality

Cites Work

• Zeros of analytic functions and norms of inverse matrices
• Zum Verhältnis von Volumen zu Oberfläche bei konvexen Körpern
• Verallgemeinerung eines Mittelwertsatzes von J. Favard für positive konkave Funktionen
• Information theoretic inequalities
• On a local version of the Aleksandrov-Fenchel inequality for the quermassintegrals of a convex body
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