PreprintarXiv licencearXiv
Hadwiger's Theorem on hyperbolic space
Abstract
We present a proof classifying continuous isometry invariant valuations on polytopes in hyperbolic space ℍn as linear combinations of the intrinsic volumes. The argument relies on an adaptation of the spherical case recently established by the author that circumvents an approximation step which does not generalize to the hyperbolic setting.
Related
- The topological Ax--Lindemann theorem for the complex hyperbolic space
- Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions
- Monotone Hadwiger Theorems on Spherical and Hyperbolic Convex Sets
- Tweaking the constant in the Linear Hadwiger Theorem
- The Spherical Hadwiger Theorem
BibTeX
@misc{knoerr2026hadwigers,
title = {{Hadwiger's Theorem on hyperbolic space}},
author = {Jonas Knoerr},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29716},
eprint = {2609.29716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29716},
}
RIS
TY - UNPB
TI - Hadwiger's Theorem on hyperbolic space
AU - Jonas Knoerr
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29716
UR - https://arxiv.org/abs/2609.29716
AB - We present a proof classifying continuous isometry invariant valuations on polytopes in hyperbolic space ℍ^n as linear combinations of the intrinsic volumes. The argument relies on an adaptation of the spherical case recently established by the author that circumvents an approximation step which does not generalize to the hyperbolic setting.
ER -