Stability Properties of Geometric Inequalities

DOI10.2307/2324388zbMath0721.52001OpenAlexW2088182811MaRDI QIDQ5753132

Helmut Groemer

Publication date: 1990

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2324388

zbMATH Keywords

surveystabilityisoperimetric inequalitygeometric inequalitiesplanar convex bodiesmixed areaBrunn-Minkowski Theorem

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Research exposition (monographs, survey articles) pertaining to convex and discrete geometry (52-02)

Related Items (11)

Strengthened volume inequalities for $L_p$ zonoids of even isotropic measures ⋮ Bonnesen-style inequalities and pseudo-perimeters for polygons ⋮ Isotropic measures and stronger forms of the reverse isoperimetric inequality ⋮ A mixed symmetric Chernoff type inequality and its stability properties ⋮ The planar Busemann-Petty centroid inequality and its stability ⋮ Stability Results for First Order Projection Bodies ⋮ Strengthened inequalities for the mean width and the ℓ‐norm ⋮ Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit ⋮ Stability of a reverse isoperimetric inequality ⋮ Stabilities of the generalized mixed width and dual mixed radial inequalities ⋮ Stability of the Blaschke-Santaló inequality in the plane

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