Integral geometry for the 1-norm

DOI10.1016/j.aam.2012.02.002zbMath1252.53088arXiv1012.5881OpenAlexW1988814836MaRDI QIDQ444426

Tom Leinster

Publication date: 14 August 2012

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

Full work available at URL: https://arxiv.org/abs/1012.5881

zbMATH Keywords

metric spaceconvex setvaluationkinematic formulageodesic space1-normcrofton formulaHadwiger's theoremSteiner's theoremtaxicab metric

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Metric geometry (51F99) Integral geometry (53C65) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (2)

Magnitude and Holmes–Thompson intrinsic volumes of convex bodies ⋮ Spaces of extremal magnitude

Cites Work

• Valuations on manifolds and integral geometry
• Hermitian integral geometry
• Valuations with Crofton formula and Finsler geometry
• Continuous translation invariant valuations on the space of compact convex sets
• Integral geometry in Minkowski spaces
• Restricted-orientation convexity.
• On P. McMullen's conjecture on translation invariant valuations
• Theory of valuations on manifolds: A survey
• Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
• Crofton formulas in projective Finsler spaces
• A short proof of Hadwiger's characterization theorem
• Metric spaces, convexity and nonpositive curvature
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture
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