Centered Bodies and Dual Mixed Volumes
From MaRDI portal
Publication:4316967
DOI10.2307/2154998zbMath0812.52005OpenAlexW4254502176MaRDI QIDQ4316967
Publication date: 19 December 1994
Full work available at URL: https://doi.org/10.2307/2154998
Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (61)
Christoffel-Minkowski flows ⋮ Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies ⋮ The dual \(\phi\)-Brunn-Minkowski inequality ⋮ Functional analytic characterizations of classes of convex bodies ⋮ New inequalities for star bodies ⋮ On intersection and mixed intersection bodies ⋮ Dual Orlicz-Brunn-Minkowski theory: dual Orlicz \(L_{\phi}\) affine and geominimal surface areas ⋮ Cross $i$-sections of star bodies and dual mixed volumes ⋮ \((p,q)\)-mixed geominimal surface area and \((p,q)\)-mixed affine surface area ⋮ Busemann-Petty problem for the i-th radial Blaschke-Minkowski homomorphisms ⋮ Extremum problems for the cone volume functional of convex polytopes ⋮ \(L_p\)-mixed intersection bodies and star duality ⋮ \(q\)-dual mixed volumes and \(L_{p}\)-intersection bodies ⋮ Dual Orlicz-Brunn-Minkowski theory ⋮ Complex \(L_p\)-intersection bodies ⋮ Lutwak-Petty projection inequalities for Minkowski valuations and their duals ⋮ The Orlicz centroid inequality for star bodies ⋮ Stability and slicing inequalities for intersection bodies ⋮ A hyperplane inequality for measures of convex bodies in \(\mathbb R^{n }, \; n\leq 4\) ⋮ Volume extremals of general L_p-centroid bodies ⋮ Stability related to the Lp$L_p$ Busemann–Petty problem ⋮ On the dual Orlicz mixed volumes ⋮ Stability of volume comparison for complex convex bodies ⋮ Stability in the Busemann-Petty and Shephard problems ⋮ Starshaped sets ⋮ Cyclic Brunn-Minkowski inequalities for dual mixed volumes ⋮ Autour de l'inégalité de Brunn-Minkowski ⋮ The dual generalized Chernoff inequality for star-shaped curves ⋮ Valuations and Busemann-Petty type problems ⋮ On the generalized Busemann-Petty problem ⋮ On dual quermassintegrals of mixed intersection bodies ⋮ A generalized funk’s section theorem for measures ⋮ \(L_{p}\) dual curvature measures ⋮ The \(L_p\)-curvature images of convex bodies and \(L_p\)-projection bodies ⋮ On the local equatorial characterization of zonoids and intersection bodies ⋮ Brunn-Minkowski inequalities for star duals of intersection bodies and two additions ⋮ On star duality of mixed intersection bodies ⋮ On reverses of the L p -Busemann-Petty centroid inequality and its applications ⋮ Dual \(L_p\)-mixed geominimal surface area and related inequalities ⋮ Generalized intersection bodies are not equivalent ⋮ Intersection Bodies and the Busemann-Petty Problem ⋮ Volume Inequalities and Additive Maps of Convex Bodies ⋮ Brunn-Minkowski inequality for mixed intersection bodies ⋮ Inequalities for dual quermassintegrals of mixed intersection bodies ⋮ The Busemann-Petty problem for arbitrary measures ⋮ Mixed \(L_p\) projection inequality ⋮ Estimating volume and surface area of a convex body via its projections or sections ⋮ Isomorphic Busemann-Petty problem for sections of proportional dimensions ⋮ Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3 ⋮ On Brunn-Minkowski type inequality ⋮ A classification of some unit Lorentz balls as non-intersection bodies ⋮ \(L_{p}\)-mixed intersection bodies ⋮ On the Negative Solutions of L_p-Busemann-Petty Problem ⋮ A generalization of the Busemann-Petty problem on sections of convex bodies ⋮ A new ellipsoid associated with convex bodies ⋮ The Cramer-Rao inequality for star bodies ⋮ Stability estimates for star bodies in terms of their intersection bodies ⋮ Convex intersection bodies in three and four dimensions ⋮ Dual kinematic formulas ⋮ Extreme properties of quermassintegrals of convex bodies ⋮ On dual mixed quermassintegral quotient functions
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
- Unnamed Item
- Minkowski's and related problems for convex surfaces with boundaries
- Centroid surfaces
- Centrally symmetric convex bodies and the spherical Radon transform
- Mixed affine surface area
- Intersection bodies and dual mixed volumes
- On surface area measures of convex bodies
- \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
- On the Busemann-Petty problem for perturbations of the ball
- Centrally symmetric convex bodies and distributions
- Centrally symmetric convex bodies and distributions. II
- A positive answer to the Busemann-Petty problem in three dimensions
- Dual mixed volumes
- Functional analytic characterizations of classes of convex bodies
- Zu einem Problem von Shephard über die Projektionen konvexer Körper
- Problems on convex bodies
- A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies
- Centroid Bodies and Dual Mixed Volumes
- Volume of Mixed Bodies
- The existence of a centrally symmetric convex body with central sections that are unexpectedly small
- Elliptic Partial Differential Equations of Second Order
- On the regularity of the solution of then-dimensional Minkowski problem
- Centrally symmetric convex sets and mixed volumes
- Intersection Bodies and the Busemann-Petty Problem
- Characterizations and Inequalities for Zonoids
- Sets of Constant Relative Width and Constant Relative Brightness
- A Class of Convex Bodies
- Infinitesimal Aspects of the Busemann-Petty Problem
- A Theorem on Convex Bodies of the Brunn-Minkowski Type
- On the Third Fundamental Form of a Surface
- The Weyl and Minkowski problems in differential geometry in the large
- Convexity
This page was built for publication: Centered Bodies and Dual Mixed Volumes
