Combinatorial integral geometry, metrics, and zonoids

DOI10.1007/BF00580819zbMath0624.52002OpenAlexW4253241985MaRDI QIDQ578589

Rouben V. Ambartsumian

Publication date: 1987

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00580819

zbMATH Keywords

combinatorial integral geometryreconstruction from projectionsmean curvature integralwedges\(\sin ^ 2\)-representation of breadth functions of convex bodiesk-zonoidstranslation invariant measures

Mathematics Subject Classification ID

Integral geometry (53C65) Other problems of combinatorial convexity (52A37) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (18)

Solution of an integral equation by consistency method ⋮ A flag representation of projection functions ⋮ A synopsis of combinatorial integral geometry ⋮ Measures in the space of planes and convex bodies ⋮ Tomography models of random convex polygons ⋮ On continuity of Buffon functionals in the space of planes in \(\mathbb{R}^3\) ⋮ Generalized radon transform on the sphere ⋮ Conditional moments for a \(d\)-dimensional convex body ⋮ Integration of combinatorial decompositions in the presence of collinearities ⋮ Combinatorial principles in stochastic geometry in the plane: A review ⋮ Flag Measures for Convex Bodies ⋮ EXTENSIONS OF TRANSLATION INVARIANT VALUATIONS ON POLYTOPES ⋮ Unnamed Item ⋮ To local reconstruction from the spherical mean Radon transform ⋮ A description of linearly additive metrics on $\mathbb {R}^n$ ⋮ A flag representation for a \(n\)-dimensional convex body ⋮ A representation for the generating density of convex bodies ⋮ The sine representation of centrally symmetric convex bodies

Cites Work

• A synopsis of combinatorial integral geometry
• The number of partitions of a set of N points in k dimensions induced by hyperplanes
• On partitions of N points
• The solution to the Buffon-Sylvester problem inR 3
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• Unnamed Item
• Unnamed Item
• Unnamed Item

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