Crofton measures and Minkowski valuations
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Publication:986631
DOI10.1215/00127094-2010-033zbMath1205.52004arXiv1207.7254OpenAlexW2125314339MaRDI QIDQ986631
Publication date: 11 August 2010
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1207.7254
convex bodyequivariantvaluationintrinsic volumeMinkowski valuationCrofton measurerigid motion invariant
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)
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Cites Work
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- Theory of valuations on manifolds. II
- Valuations on manifolds and Rumin cohomology
- Valuations with Crofton formula and Finsler geometry
- Convolution of convex valuations
- Valuations and Busemann-Petty type problems
- A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
- A Hadwiger-type theorem for the special unitary group
- Continuous rotation invariant valuations on convex sets
- Ellipsoids and matrix-valued valuations
- A new ellipsoid associated with convex bodies
- \(L_ p\) affine isoperimetric inequalities.
- Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
- Range characterization of the cosine transform on higher Grassmannians
- Valuations on polytopes containing the origin in their interiors
- Projection bodies and valuations
- The multiplicative structure on continuous polynomial valuations
- An Euler relation for valuations on polytopes
- A characterization of affine surface area
- Theory of valuations on manifolds. I: Linear spaces
- Volume inequalities for subspaces of \(L_p\)
- Structure of the unitary valuation algebra
- Inequalities for Mixed Projection Bodies
- Mixed Projection Inequalities
- Intersection bodies and valuations
- A characterization of Lp intersection bodies
- Blaschke- and Minkowski-endomorphisms of convex bodies
- Rotation equivariant Minkowski valuations
- Canonical Extensions of Harish-Chandra Modules to Representations of G
- Stochastic and Integral Geometry
- Convolutions and multiplier transformations of convex bodies
- Star body valued valuations
- Convolutions, Transforms, and Convex Bodies
- The determination of convex bodies from the mean of random sections
- Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
- Even valuations on convex bodies
- Equivariant Endomorphisms of the Space of Convex Bodies
- Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure
- Volume Inequalities and Additive Maps of Convex Bodies
- Theory of valuations on manifolds, III. Multiplicative structure in the general case
- Minkowski valuations
- Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture