Does polynomial parallel volume imply convexity?

DOI10.1007/s00208-003-0497-7zbMath1048.52003OpenAlexW2005706098MaRDI QIDQ1434158

Günter Last, Matthias Heveling, Daniel Hug

Publication date: 1 July 2004

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-003-0497-7

zbMATH Keywords

convex bodiesSteiner formulaparallel body

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38)

Related Items (9)

Polynomial volume estimation and its applications ⋮ On mean curvature functions of Brownian paths ⋮ A geometrically motivated parametric model in manifold estimation ⋮ Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets ⋮ Minkowski tensors of anisotropic spatial structure ⋮ Polynomial parallel volume, convexity and contact distributions of random sets ⋮ The parallel volume at large distances ⋮ Local empirical processes near boundaries of convex bodies ⋮ The derivative of the parallel volume difference

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