Generalized intersection bodies

DOI10.1016/j.jfa.2006.04.004zbMath1109.52006arXivmath/0512058OpenAlexW2004501929MaRDI QIDQ860791

Emanuel Milman

Publication date: 9 January 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512058

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Integral geometry (53C65) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (34)

A Remark on Measures of Sections of $$\boldsymbol{L}_{p}$$ -balls ⋮ Projection functions, area measures and the Alesker-Fourier transform ⋮ Inequalities for the derivatives of the Radon transform on convex bodies ⋮ Cross $i$-sections of star bodies and dual mixed volumes ⋮ On sections of convex bodies in hyperbolic space ⋮ Comparison of volumes of convex bodies in real, complex, and quaternionic spaces ⋮ The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry ⋮ Counterexamples to convexity of $k$-intersection bodies ⋮ The lower dimensional Busemann-Petty problem in the complex hyperbolic space ⋮ Complex \(L_p\)-intersection bodies ⋮ Stability and slicing inequalities for intersection bodies ⋮ Intersection bodies and generalized cosine transforms ⋮ Stability related to the Lp$L_p$ Busemann–Petty problem ⋮ Adams inequalities on measure spaces ⋮ On strict inclusions in hierarchies of convex bodies ⋮ Isomorphic properties of intersection bodies ⋮ Sections of convex bodies with symmetries ⋮ On the generalized Busemann-Petty problem ⋮ A generalized funk’s section theorem for measures ⋮ Generalized intersection bodies are not equivalent ⋮ On an analytic generalization of the Busemann-Petty problem ⋮ Positive definite distributions and normed spaces ⋮ An isomorphic version of the Busemann-Petty problem for arbitrary measures ⋮ The complex Busemann-Petty problem on sections of convex bodies ⋮ Local properties of intertwining operators on the sphere ⋮ The Lower Dimensional Busemann‐Petty Problem with Weights ⋮ Slicing inequalities for subspaces of $L_p$ ⋮ Slicing inequalities for measures of convex bodies ⋮ Isomorphic Busemann-Petty problem for sections of proportional dimensions ⋮ Bounding marginal densities via affine isoperimetry ⋮ A Fourier transform approach to Christoffel’s problem ⋮ The Busemann-Petty problem on entropy of log-concave functions ⋮ A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury's identity ⋮ A note on 𝑘-intersection bodies

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