Kinematic formulas for tensor valuations

DOI10.1515/crelle-2015-0023zbMath1501.53084arXiv1402.2750OpenAlexW3099940774MaRDI QIDQ1703669

Andreas Bernig, Daniel Hug

Publication date: 7 March 2018

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2750

zbMATH Keywords

convolutionCrofton formulasAlesker-Fourier transformtensor valuations

Mathematics Subject Classification ID

Computational aspects related to convexity (52B55) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Integral geometry (53C65) Lie groups (22E99) Dissections and valuations (Hilbert's third problem, etc.) (52B45)

Related Items (28)

Integral Geometry and Algebraic Structures for Tensor Valuations ⋮ Crofton Formulae for Tensor-Valued Curvature Measures ⋮ Rotation Invariant Valuations ⋮ On Hodge-Riemann relations for translation-invariant valuations ⋮ Local tensor valuations ⋮ Projection functions, area measures and the Alesker-Fourier transform ⋮ Additive kinematic formulas for flag area measures ⋮ Surface tensor estimation from linear sections ⋮ Spin-invariant valuations on the octonionic plane ⋮ Minkowski valuations under volume constraints ⋮ Rotational Crofton formulae for Minkowski tensors and some affine counterparts ⋮ Tensor valuations on lattice polytopes ⋮ On mixed Hodge–Riemann relations for translation-invariant valuations and Aleksandrov–Fenchel inequalities ⋮ Rotation covariant local tensor valuations on convex bodies ⋮ Vectorial analogues of Cauchy's surface area formula ⋮ Generalized translation invariant valuations and the polytope algebra ⋮ From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies ⋮ Minkowski additive operators under volume constraints ⋮ Dimension of the space of unitary equivariant translation invariant tensor valuations ⋮ \(\mathrm{SL}(m, \mathbb{C})\)-equivariant and translation covariant continuous tensor valuations ⋮ Kinematic formulae for tensorial curvature measures ⋮ Centro-affine tensor valuations ⋮ Contact measures in isotropic spaces ⋮ Integral geometry of unitary area measures ⋮ Uniqueness of the measurement function in Crofton's formula ⋮ Dual area measures and local additive kinematic formulas ⋮ Characterisation of valuations and curvature measures in euclidean spaces ⋮ LYZ Matrices and SL() Contravariant Valuations on Polytopes

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