Volume of Mixed Bodies

DOI10.2307/2000195zbMath0591.52016OpenAlexW4250862308MaRDI QIDQ3719398

Erwin Lutwak

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000195

zbMATH Keywords

isoperimetric inequalitiesconvex bodyprojection bodieszonoidsmixed area measureprojection measuresQuermassintegralevolume of mixed bodies

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) 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 (38)

\(L_{p}\)-dual geominimal surface area and general \(L_{p}\)-centroid bodies ⋮ Orlicz-Aleksandrov-Fenchel inequality for Orlicz multiple mixed volumes ⋮ On intersection and mixed intersection bodies ⋮ The Brunn-Minkowski inequality ⋮ Rotation means of projections ⋮ Mixed affine surface area ⋮ The Petty projection inequality for \(L_p\)-mixed projection bodies ⋮ Projection problems for symmetric polytopes ⋮ \(L_{p}\)-Aleksandrov-Fenchel inequality ⋮ Intersection bodies and dual mixed volumes ⋮ Some inequalities for geominimal surface areas ⋮ On Blaschke-Minkowski homomorphisms ⋮ On radial Blaschke-Minkowski homomorphisms ⋮ \(q\)-dual mixed volumes and \(L_{p}\)-intersection bodies ⋮ Divergence-Free Tensors and Cofactors in Geometry and Fluid Dynamics ⋮ The affine log-Aleksandrov–Fenchel inequality ⋮ Lutwak-Petty projection inequalities for Minkowski valuations and their duals ⋮ Convex set symmetry measurement using Blaschke addition ⋮ Spherical centroid bodies ⋮ Volume inequalities for the \(i\)-th-convolution bodies ⋮ Inequalities for Mixed Projection Bodies ⋮ On dual quermassintegrals of mixed intersection bodies ⋮ Subword complexity and projection bodies ⋮ \(L_{p}\)-Brunn-Minkowski inequality ⋮ Projection bodies in complex vector spaces ⋮ Volume Inequalities and Additive Maps of Convex Bodies ⋮ Brunn-Minkowski inequality for mixed intersection bodies ⋮ Mixed \(L_p\) projection inequality ⋮ Inequalities for polars of mixed projection bodies ⋮ The planar Busemann-Petty centroid inequality and its stability ⋮ Centered Bodies and Dual Mixed Volumes ⋮ Dual Orlicz geominimal surface area ⋮ Some \(\log\)-Minkowski inequalities for \(L_p\)-mixed affine surface area ⋮ Dual Orlicz mixed geominimal surface area ⋮ \(L_{p}\)-mixed intersection bodies ⋮ The Brunn-Minkowski type inequalities for mixed brightness-integrals ⋮ Enumerating a subset of the integer points inside a Minkowski sum ⋮ On LYZ's conjecture for the \(U\)-functional

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minkowski's and related problems for convex surfaces with boundaries
• Centroid surfaces
• A generalization of Minkowski's inequality for plane convex sets
• Mixed width-integrals of convex bodies
• Über einige Eindeutigkeitssätze für konvexe Körper
• Über Tangentialkörper der Kugel
• Addition and decomposition of convex polytopes
• The mean volume of boxes and cylinders circumscribed about a convex body
• Isoperimetric inequalities for the mean width of a convex body
• Mixed Projection Inequalities
• A General Isepiphanic Inequality
• Geometric Inequalities for Plane Convex Bodies
• Width-Integrals of Convex Bodies
• Sets of Constant Relative Width and Constant Relative Brightness
• A Class of Convex Bodies

This page was built for publication: Volume of Mixed Bodies