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arXiv · 2609.17437

Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions

Martin Lotz
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Abstract

We give an elementary and combinatorial proof of the spherical Hadwiger theorem, which states that every continuous, rotation-invariant valuation on the space of closed convex cones in $\R^n$ is a linear combination of the conic intrinsic volumes. Our proof uses a signed orthoscheme decomposition. Its vanishing step requires only integrability of an orthoscheme restriction of the residual valuation, a weaker regularity condition than continuity.

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Martin Lotz. 2026-09-15. Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions. https://arxiv.org/abs/2609.17437

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