Convolutions and multiplier transformations of convex bodies
From MaRDI portal
Publication:3595032
DOI10.1090/S0002-9947-07-04270-5zbMath1156.52003arXiv1207.7252OpenAlexW2005347511MaRDI QIDQ3595032
Publication date: 9 August 2007
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1207.7252
spherical harmonicconvex bodyprojection bodyMinkowski additionBlaschke additionmultiplier transformationspherical convolutionPetty conjecturerotation intertwining map
Inequalities and extremum problems involving convexity in convex geometry (52A40) Harmonic analysis and spherical functions (43A90) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items
A Hadwiger-Type Theorem for General Tensor Valuations ⋮ Projection functions, area measures and the Alesker-Fourier transform ⋮ Minkowski endomorphisms ⋮ On Blaschke-Minkowski homomorphisms and radial Blaschke-Minkowski homomorphisms ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds ⋮ On the inverse Klain map ⋮ On Blaschke-Minkowski homomorphisms ⋮ Extremum problems for the cone volume functional of convex polytopes ⋮ On radial Blaschke-Minkowski homomorphisms ⋮ \(L_p\) Blaschke-Minkowski homomorphisms ⋮ The 3-ball is a local pessimum for packing ⋮ On \(p\)-radial Blaschke and harmonic Blaschke additions ⋮ Lutwak-Petty projection inequalities for Minkowski valuations and their duals ⋮ Iterations of Minkowski valuations ⋮ The Steiner formula for Minkowski valuations ⋮ Radial Blaschke--Minkowski homomorphisms and volume differences ⋮ Equivariant endomorphisms of convex functions ⋮ Minkowski additive operators under volume constraints ⋮ A characterization of Blaschke addition ⋮ General \(L_{p}\)-harmonic Blaschke bodies ⋮ General Lp-mixed width-integral of convex bodies and related inequalities ⋮ Valuations and Busemann-Petty type problems ⋮ Log-concavity properties of Minkowski valuations ⋮ Fixed points of Minkowski valuations ⋮ On radial and polar Blaschke-Minkowski homomorphisms ⋮ Subword complexity and projection bodies ⋮ Orlicz-Brunn-Minkowski inequalities for Blaschke-Minkowski homomorphisms ⋮ Asymmetric $L_p$-difference bodies ⋮ Monotonicity inequalities for Blaschke-Minkowski homomorphisms ⋮ Pessimal packing shapes ⋮ Crofton measures and Minkowski valuations ⋮ Harmonic analysis of translation invariant valuations ⋮ General \(L_{p}\)-mixed chord integrals of star bodies ⋮ Radial Minkowski additive operators ⋮ ISOPERIMETRIC INEQUALITIES FOR Lp GEOMINIMAL SURFACE AREA ⋮ Affine vs. Euclidean isoperimetric inequalities ⋮ Minkowski valuations on $L^{p}$-spaces ⋮ $\mathrm{GL}(n)$ contravariant Minkowski valuations ⋮ Shephard Type Problem for Lp-mixed Blaschke-Minkowski homomorphisms ⋮ When is the ball a local pessimum for covering? ⋮ Volume sums of polar Blaschke-Minkowski homomorphisms
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On quermassintegrals of mixed projection bodies
- On the intermediate area functions of convex bodies
- Continuous translation invariant valuations on the space of compact convex sets
- On surface area measures of convex bodies
- Kontinuierliche Linearkombination von Strecken
- Bewegungsäquivariante, additive und stetige Transformationen konvexer Bereiche
- Projection bodies and valuations
- Zu einem Problem von Shephard über die Projektionen konvexer Körper
- Inequalities for Mixed Projection Bodies
- Mixed Projection Inequalities
- Blaschke- and Minkowski-endomorphisms of convex bodies
- Convolutions, Transforms, and Convex Bodies
- The determination of convex bodies from the mean of random sections
- Equivariant Endomorphisms of the Space of Convex Bodies
- Über den Vektorraum der Differenzen von Stützfunktionen konvexer Körper
- Volume Inequalities and Additive Maps of Convex Bodies
- Minkowski valuations
- A Class of Convex Bodies