Hadwiger's Theorem on hyperbolic space

Abstract

We present a proof classifying continuous isometry invariant valuations on polytopes in hyperbolic space ${\mathbb{H}}^n$ 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.

arXiv comment18 pages