On the Affine Surface Area
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Publication:3134700
DOI10.2307/2160080zbMath0784.52004OpenAlexW4239689452MaRDI QIDQ3134700
Publication date: 13 September 1993
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2160080
Hausdorff measureconvex bodiesvaluationGauss-Kronecker curvatureaffine surface areasupporting hyperplane
Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Affine differential geometry (53A15)
Related Items (27)
The spherical convex floating body ⋮ Contributions to affine surface area ⋮ Equality of two representations of extended affine surface area ⋮ \(L_{p}\)-mixed affine surface area ⋮ Constrained convex bodies with extremal affine surface areas ⋮ The generalized \(L_p\)-mixed affine surface area ⋮ Geometric valuation theory ⋮ \(L_p\)-Steiner quermassintegrals ⋮ Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality ⋮ On bodies floating in equilibrium in every orientation ⋮ The floating body and the hyperplane conjecture ⋮ Deviation inequalities for random polytopes in arbitrary convex bodies ⋮ Stability of the Blaschke-Santaló and the affine isoperimetric inequality ⋮ A characterization of affine surface area ⋮ A characterization of affine length and asymptotic approximation of convex discs ⋮ \(L_p\)-dual affine surface area ⋮ A new type of Brunn-Minkowski inequality for affine surface area and its applications ⋮ A generalized affine isoperimetric inequality ⋮ General affine surface areas ⋮ Affine restriction for radial surfaces ⋮ Ulam floating bodies ⋮ The Santaló-regions of a convex body ⋮ On the \(p\)-affine surface area ⋮ An affine restriction estimate in $\mathbb{R}^3$ ⋮ An integral formula for the total mean curvature matrix ⋮ The \(i\)th \(p\)-geominimal surface area ⋮ The \(i\)th \(p\)-affine surface area
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