Equivariant Endomorphisms of the Space of Convex Bodies

DOI10.2307/1996793zbMath0287.52004OpenAlexW4249895454MaRDI QIDQ4775088

Rolf Schneider

Publication date: 1974

Full work available at URL: https://doi.org/10.2307/1996793

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (37)

A Hadwiger-Type Theorem for General Tensor Valuations ⋮ Minkowski endomorphisms ⋮ Minkowski valuations under volume constraints ⋮ On the inverse Klain map ⋮ On monotone translation-projection covariant Minkowski valuations ⋮ The role of the Rogers-Shephard inequality in the characterization of the difference body ⋮ Geometric valuation theory ⋮ Lutwak-Petty projection inequalities for Minkowski valuations and their duals ⋮ Intersection bodies and ellipsoids ⋮ Rotation Invariant Minkowski Classes of Convex Bodies ⋮ Iterations of Minkowski valuations ⋮ The Steiner formula for Minkowski valuations ⋮ Equivariant endomorphisms of convex functions ⋮ Minkowski additive operators under volume constraints ⋮ Attitude toward imprecise information ⋮ Simple valuations on convex bodies ⋮ Valuations and Busemann-Petty type problems ⋮ Diagonal Minkowski classes, zonoid equivalence, and stable laws ⋮ Log-concavity properties of Minkowski valuations ⋮ Fixed points of Minkowski valuations ⋮ Volume Inequalities and Additive Maps of Convex Bodies ⋮ Einschachtelung konvexer Körper ⋮ Convolutions and multiplier transformations of convex bodies ⋮ Crofton measures and Minkowski valuations ⋮ Radial Minkowski additive operators ⋮ Even valuations on convex bodies ⋮ Minkowski valuations ⋮ General \((p,q)\)-mixed projection bodies ⋮ Smooth approximation of convex bodies ⋮ Refined Euler-Lagrange inclusion for an optimal control problem with discontinuous integrand ⋮ Affine vs. Euclidean isoperimetric inequalities ⋮ Dualities and endomorphisms of pseudo-cones ⋮ $\mathrm{GL}(n)$ contravariant Minkowski valuations ⋮ 𝐿_{𝑝}-Blaschke valuations ⋮ Blaschke- and Minkowski-endomorphisms of convex bodies ⋮ Bewegungsäquivariante, additive und stetige Transformationen konvexer Bereiche ⋮ Projection bodies and valuations

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