A stability estimate for the Aleksandrov-Fenchel inequality, with an application to mean curvature

DOI10.1007/BF02567927zbMath0713.52003MaRDI QIDQ749868

Rolf Schneider

Publication date: 1990

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155560

zbMATH Keywords

Hausdorff metricmixed volumemean curvatureconvex bodiesAleksandrov-Fenchel inequality

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 (10)

Reverse Alexandrov–Fenchel inequalities for zonoids ⋮ The improved isoperimetric inequality and the Wigner caustic of planar ovals ⋮ Diameter bounds for convex surfaces with pinched mean curvature ⋮ On the Shape of Compact Hypersurfaces with Almost-Constant Mean Curvature ⋮ Quantitative estimates for almost constant mean curvature hypersurfaces ⋮ A mixed symmetric Chernoff type inequality and its stability properties ⋮ Stability of a reverse isoperimetric inequality ⋮ On the Aleksandrov--Fenchel inequality and the stability of the sphere ⋮ Stability of inequalities in the dual Brunn-Minkowski theory ⋮ Curvature measures and stability

Cites Work

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• On the Aleksandrov-Fenchel inequality for convex bodies. I
• \(L_p\) metrics for compact convex sets
• On Blaschke's rolling theorems
• Almost Spherical Convex Hypersurfaces
• Stability Results for First Order Projection Bodies
• Stability Estimates for some Geometric Inequalities
• Stability in the Aleksandrov‐Fenchel‐Jessen Theorem
• Ovaloids which are almost spheres

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