Integral geometry of tensor valuations

DOI10.1016/j.aam.2008.04.001zbMath1158.52004OpenAlexW2106190248MaRDI QIDQ953900

Rolf Schneider, Ralph Schuster, Daniel Hug

Publication date: 6 November 2008

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2008.04.001

zbMATH Keywords

convex bodyintegral geometryintrinsic volumeMinkowski tensortensor valuationCrofton formula

Mathematics Subject Classification ID

Integral geometry (53C65) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items

Tensor Valuations and Their Local Versions, Integral Geometry and Algebraic Structures for Tensor Valuations, Crofton Formulae for Tensor-Valued Curvature Measures, A Hadwiger-Type Theorem for General Tensor Valuations, Rotation Invariant Valuations, Reconstruction of convex bodies from surface tensors, Local tensor valuations, Additive kinematic formulas for flag area measures, Surface tensor estimation from linear sections, Rotational Crofton formulae for Minkowski tensors and some affine counterparts, Local tensor valuations on convex polytopes, Minkowski tensor density formulas for Boolean models, The invariator principle in convex geometry, Poisson Point Process Convergence and Extreme Values in Stochastic Geometry, Rotation covariant local tensor valuations on convex bodies, Mean surface and volume particle tensors under \(L\)-restricted isotropy and associated ellipsoids, Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor, Vectorial analogues of Cauchy's surface area formula, Kinematic formulas for tensor valuations, A flag representation of projection functions, Classification of invariant valuations on the quaternionic plane, Local stereology of tensors of convex bodies, Distances between Poisson \(k\)-flats, Minkowski tensors of anisotropic spatial structure, Kinematic formulae for tensorial curvature measures, Voronoi-based estimation of Minkowski tensors from finite point samples, Difference bodies in complex vector spaces, Expressing intrinsic volumes as rotational integrals, Centro-affine tensor valuations, Contact measures in isotropic spaces, Harmonic analysis of translation invariant valuations, Intersection probabilities and kinematic formulas for polyhedral cones, Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry, Integral geometry of unitary area measures, Intersection and proximity of processes of flats, Integral geometric inequalities and valuations, The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals, Valuations on function spaces, Characterisation of valuations and curvature measures in euclidean spaces, LYZ Matrices and SL() Contravariant Valuations on Polytopes

Cites Work

• Description of continuous isometry covariant valuations on convex sets
• Continuous rotation invariant valuations on convex sets
• Absolute continuity for curvature measures of convex sets. II
• Vektorielle Integralgeometrie
• Krümmungsschwerpunkte konvexer Körper. I. (Barycenters of curvature of convex bodies. I.)
• Integral Geometry in Statistical Physics
• Translative and Kinematic Formulae for Curvature Measures of Flat Sections
• The space of isometry covariant tensor valuations
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