27 citations · 34 across the 18 of their papers we have counts for
4 papers · 2 filters
Hadwiger's Theorem on hyperbolic space
Jonas Knoerr
We present a proof classifying continuous isometry invariant valuations on polytopes in hyperbolic space as linear combinations of the intrinsic volumes. The argumen…
Isometry invariant valuations on spherical polytopes
Jonas Knoerr
We show that every continuous and isometry invariant valuation on spherical polytopes is a linear combination of the spherical intrinsic volumes. The proof relies on a weak differe…
Rigid motion invariant valuations on polytopes
Jonas Knoerr
We show that any measurable, translation and -invariant valuation on polytopes in is a linear combination of the intrinsic volumes, which extends Had…
Translation invariant area measures on convex bodies
Jonas Knoerr
We introduce the space of continuous and translation invariant area measures, which are measure-valued functionals on the space of convex bodies satisfying a certain locality condi…