Valuations on manifolds and integral geometry

DOI10.1007/s00039-010-0088-1zbMath1213.52013arXiv0905.4046OpenAlexW2002691267MaRDI QIDQ607662

Semyon Alesker

Publication date: 3 December 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.4046

zbMATH Keywords

manifoldsRadon transformvaluationspull-backpush-forward

Mathematics Subject Classification ID

Radon transform (44A12) Integral geometry (53C65) Mixed volumes and related topics in convex geometry (52A39) Dissections and valuations (Hilbert's third problem, etc.) (52B45)

Related Items (24)

Valuations and Curvature Measures on Complex Spaces ⋮ On Repeated Sequential Closures of Constructible Functions in Valuations ⋮ Valuation theory of indefinite orthogonal groups ⋮ Crofton formulas and indefinite signature ⋮ Classification of angular curvature measures and a proof of the angularity conjecture ⋮ The Weyl principle on the Finsler frontier ⋮ Crofton formulas in pseudo-Riemannian space forms ⋮ The spherical convex floating body ⋮ Curvature measures of pseudo-Riemannian manifolds ⋮ The Centro-Affine Hadwiger Theorem ⋮ On the inverse Klain map ⋮ Uniqueness of curvature measures in pseudo-Riemannian geometry ⋮ On the extendability by continuity of angular valuations on polytopes ⋮ Hadwiger's theorem for definable functions ⋮ Integral geometry for the 1-norm ⋮ On extendability by continuity of valuations on convex polytopes ⋮ Functional properties of Hörmander's space of distributions having a specified wavefront set ⋮ Integral geometry of complex space forms ⋮ Positivity of valuations on convex bodies and invariant valuations by linear actions ⋮ Contact integral geometry and the Heisenberg algebra ⋮ Natural operations on differential forms on contact manifolds ⋮ Integral geometric inequalities and valuations ⋮ Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker) ⋮ Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3

Cites Work

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