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PreprintCC BY 4.0arXiv

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 Rn 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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Cite

BibTeXRIS
BibTeX
@misc{lotz2026hadwigers,
  title = {{Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions}},
  author = {Martin Lotz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17437},
  eprint = {2609.17437},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17437},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions
AU  - Martin Lotz
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17437
UR  - https://arxiv.org/abs/2609.17437
AB  - 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.
ER  -