Minkowski valuations on lattice polytopes

  • Károly J. Böröczky

    Hungarian Academy of Sciences, Budapest, Hungary
  • Monika Ludwig

    Technische Universität Wien, Austria
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Abstract

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.

Cite this article

Károly J. Böröczky, Monika Ludwig, Minkowski valuations on lattice polytopes. J. Eur. Math. Soc. 21 (2019), no. 1, pp. 163–197

DOI 10.4171/JEMS/833