Curvature relations and affine surface area for a general convex body and its polar

DOI10.1007/BF03322221zbMath0861.52003MaRDI QIDQ1921416

Daniel Hug

Publication date: 27 August 1996

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

polar body\(p\)-affine surface areaequiaffine support functiongeneralized Gauss curvature

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Affine differential geometry (53A15)

Related Items (21)

A unified flow approach to smooth, even \(L_p\)-Minkowski problems ⋮ Deforming a hypersurface by Gauss curvature and support function ⋮ THE VOLUME OF RANDOM POLYTOPES CIRCUMSCRIBED AROUND A CONVEX BODY ⋮ On the stability of the \(L_p\)-curvature ⋮ Differential analysis of polarity: polar Hamilton-Jacobi, conservation laws, and Monge Ampère equations ⋮ The \(L_p\) chord Minkowski problem ⋮ New \(L_p\) affine isoperimetric inequalities ⋮ Nakajima's Problem: Convex Bodies of Constant Width and Constant Brightness ⋮ Rényi divergence and \(L_p\)-affine surface area for convex bodies ⋮ Divergence for \(s\)-concave and log concave functions ⋮ Extremal general affine surface areas ⋮ Intrinsic volumes of random polytopes with vertices on the boundary of a convex body ⋮ \(\mathrm{SL}(n)\) invariant valuations on polytopes ⋮ Absolute continuity for curvature measures of convex sets. III ⋮ Inequalities for mixed \(p\)-affine surface area ⋮ General affine surface areas ⋮ The planar Busemann-Petty centroid inequality and its stability ⋮ Unnamed Item ⋮ An application of dual convex bodies to the inverse Gauss curvature flow ⋮ On the \(p\)-affine surface area ⋮ A centro-projective inequality

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extended affine surface area
• Zur Affinoberfläche konvexer Körper. (On affine surfaces of convex bodies)
• Bestimmung konvexer Körper durch Krümmungsmaße
• Contributions to affine surface area
• The convex floating body.
• Asymptotic estimates for best and stepwise approximation of convex bodies I
• Asymptotic estimates for best and stepwise approximation of convex bodies III
• Global affine differential geometry of hypersurfaces

This page was built for publication: Curvature relations and affine surface area for a general convex body and its polar