$\mathrm {SL}(n)$-contravariant $L_p$-Minkowski valuations

DOI10.1090/S0002-9947-2013-05750-9zbMath1286.52007arXiv1410.7021OpenAlexW1589386974MaRDI QIDQ5401718

Lukas Parapatits

Publication date: 12 March 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.7021

zbMATH Keywords

polytopes\(\mathrm{SL}(n)\)-contravariant \(L_p\)-Minkowski valuationsasymmetric \(L_p\)-projection body

Mathematics Subject Classification ID

Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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Cites Work

• Unnamed Item
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• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Minkowski areas and valuations
• Projection bodies in complex vector spaces
• Hermitian integral geometry
• Invariant valuations on star-shaped sets
• Minkowski valuations intertwining the special linear group
• Ein Fortsetzungssatz für additive Eipolyederfunktionale im euklidischen Raum
• Valuations on manifolds and Rumin cohomology
• Crofton measures and Minkowski valuations
• A Hadwiger-type theorem for the special unitary group
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• Continuous rotation invariant valuations on convex sets
• Ellipsoids and matrix-valued valuations
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• A new ellipsoid associated with convex bodies
• On P. McMullen's conjecture on translation invariant valuations
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• Sharp affine \(L_ p\) Sobolev inequalities.
• The Cramer-Rao inequality for star bodies
• Valuations on polytopes containing the origin in their interiors
• Projection bodies and valuations
• Moment-entropy inequalities.
• Star valuations and dual mixed volumes
• Selection models under generalized symmetry settings
• A characterization of affine surface area
• Asymmetric affine \(L_p\) Sobolev inequalities
• New \(L_p\) affine isoperimetric inequalities
• Subword complexity and projection bodies
• Blaschke valuations
• $\mathrm{GL}(n)$ contravariant Minkowski valuations
• Intersection bodies and valuations
• A characterization of Lp intersection bodies
• Rotation equivariant Minkowski valuations
• Stochastic and Integral Geometry
• Star body valued valuations
• Even valuations on convex bodies
• $GL(n)$ equivariant Minkowski valuations
• Convex and Discrete Geometry
• Minkowski valuations
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture
• \(L_p\) intersection bodies

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