Isotropic surface area measures

DOI10.1112/S0025579300007518zbMath0960.52009MaRDI QIDQ4494736

Apostolos Giannopoulos, Michael Papadimitrakis

Publication date: 8 August 2000

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

reverse isoperimetric inequalityprojection inequalitiesisotropic surface area measureprojection and polar projection body

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40)

Related Items (42)

Continuous version of the approximate geometric Brascamp-Lieb inequalities ⋮ The characteristic properties of the minimal \(L_p\)-mean width ⋮ The logarithmic John ellipsoid ⋮ Isotropic dual p-surface area measure ⋮ Orlicz-Legendre ellipsoids ⋮ Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds ⋮ The dual Loomis–Whitney inequality ⋮ Iterations of the projection body operator and a remark on Petty's conjectured projection inequality ⋮ Strengthened volume inequalities for $L_p$ zonoids of even isotropic measures ⋮ The minimal Orlicz surface area ⋮ On the \(L_p\) affine isoperimetric inequalities ⋮ Isotropic measures and stronger forms of the reverse isoperimetric inequality ⋮ An \(\text{SL}(n)\)-invariant mixed integral \(L_p\) affine surface area ⋮ General measure extensions of projection bodies ⋮ Orlicz-John ellipsoids ⋮ Convex geometry and its connections to harmonic analysis, functional analysis and probability theory ⋮ Optimal Sobolev norms in the affine class ⋮ The minimal affine total variation on \(BV(\mathbb{R}^n)\) ⋮ A new affine invariant for polytopes and Schneider’s projection problem ⋮ New affine inequalities and projection mean ellipsoids ⋮ \((p, q)\)-John ellipsoids ⋮ Fixed points of Minkowski valuations ⋮ An extremal property of \(p\)-mean width ⋮ Gaussian inequalities for Wulff shapes ⋮ Application of an idea of Voronoĭ to John type problems ⋮ Improved regret for zeroth-order adversarial bandit convex optimisation ⋮ Strengthened inequalities for the mean width and the ℓ‐norm ⋮ Volume inequalities for complex isotropic measures ⋮ Extremal problems and isotropic positions of convex bodies ⋮ Positions of convex bodies associated to extremal problems and isotropic measures ⋮ New sine ellipsoids and related volume inequalities ⋮ Extremal problems for \(L_p\) surface areas and John ellipsoids ⋮ Comparing the M-position with some classical positions of convex bodies ⋮ On mixed \(L_{p}\) John ellipsoids ⋮ A reverse Blaschke-Santaló inequality ⋮ A sharp dual \(L_p\) John ellipsoid problem for \(p\le -n-1\) ⋮ A new ellipsoid associated with convex bodies ⋮ On the shape of a convex body with respect to its second projection body ⋮ The minimal Orlicz mean width of convex bodies ⋮ The \(L_p\) John ellipsoids for general measures ⋮ Projection bodies and valuations ⋮ The \(L_p\) Loomis-Whitney inequality

Cites Work

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• Restricted chord projection and affine inequalities
• Zonoids with minimal volume-product
• A geometric inequality with applications to linear forms
• Surface Area of a Convex Body Under Affine Transformations
• Volume Ratios and a Reverse Isoperimetric Inequality
• Zonoids with Minimal Volume-Product--A New Proof
• Shadows of Convex Bodies

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