2016/02/29 by Károly J. Böröczky, Karoly J. Boroczky, Monika Ludwig · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Covariance and contravariance of vectors #Equivariant map #Lattice (music) #Minkowski space #Morphological variations and asymmetry #Multiple #Point processes and geometric inequalities #Polytope #Special linear group #math.MG
paper · pdf · doi:10.4171/jems/833
published as J. Eur. Math. Soc. (JEMS) 21 (2019), no. 1, 163-197 · accepted in JEMS, 2016
arxiv created 2016/03/31 · openalex created_date 2016/06/24 · openalex publication_date 2018/09/21 · arxiv updated 2019/06/21 · openalex updated_date 2026/08/05
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are multiples of projection bodies. In the equivariant case, the only such valuations are generalized difference bodies combined with multiples of the newly defined discrete Steiner point.