The determination of convex bodies from the mean of random sections

DOI10.1017/S0305004100071085zbMath0772.52005MaRDI QIDQ4035893

Wolfgang Weil, Paul R. Goodey

Publication date: 16 May 1993

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

random sectionsconvex body in \(\mathbb{R}^ 3\)

Mathematics Subject Classification ID

Convex sets in (3) dimensions (including convex surfaces) (52A15) Approximation by convex sets (52A27) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (18)

A Hadwiger-Type Theorem for General Tensor Valuations ⋮ Projection functions, area measures and the Alesker-Fourier transform ⋮ On the sine polarity and the \(L_p\)-sine Blaschke-Santaló inequality ⋮ Translative and kinematic integral formulae for support functions ⋮ Directed projection functions of convex bodies ⋮ Lutwak-Petty projection inequalities for Minkowski valuations and their duals ⋮ A uniqueness result for mean section bodies ⋮ Simple valuations on convex bodies ⋮ Valuations and Busemann-Petty type problems ⋮ Log-concavity properties of Minkowski valuations ⋮ Local properties of intertwining operators on the sphere ⋮ Volume Inequalities and Additive Maps of Convex Bodies ⋮ Average section functions for star-shaped sets ⋮ Convolutions and multiplier transformations of convex bodies ⋮ Crofton measures and Minkowski valuations ⋮ Section and projection means of convex bodies ⋮ Affine vs. Euclidean isoperimetric inequalities ⋮ Minkowski sums of projections of convex bodies

Cites Work

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• Zu einem Problem von Shephard über die Projektionen konvexer Körper
• Plane polygons and a conjecture of Blaschke’s
• Translative and Kinematic Integral Formulae for Curvature Measures
• Rekonstruktion eines konvexen Körpers aus seinen Projektionen
• Über eine Integralgleichung in der Theorie der konvexen Körper
• Random secants of a convex body
• Linear-Intercept distributions do not characterize plane sets

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