From John to Gauss--John positions via dual mixed volumes

DOI10.1016/j.jmaa.2006.05.047zbMath1112.52005OpenAlexW2044682884MaRDI QIDQ864712

Jesús Bastero, Miguel Romance, Julio Bernués

Publication date: 12 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.05.047

zbMATH Keywords

dual mixed volumesKubota formula

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39)

Related Items (5)

Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds ⋮ Lower dimensional ellipsoids of maximal volume in convex bodies ⋮ Isomorphic versions of reverse isoperimetric inequalities ⋮ Mean width inequalities for isotropic measures ⋮ Extremal problems related to Gauss-John position

Cites Work

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• Ellipsoids of maximal volume in convex bodies
• Mean dual and harmonic cross-sectional measures
• Tomography of convex and star bodies
• Extremal problems and isotropic positions of convex bodies
• Positions of convex bodies associated to extremal problems and isotropic measures
• A characterization of the \(MM^*\)-position of a convex body in terms of covariance matrices
• Dual mixed volumes
• $L_p$ John Ellipsoids
• A functional analytic approach to intersection bodies

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