Characterizing addition of convex sets by polynomiality of volume and by the homothety operation

Vitali Milman, Liran Rotem

Research output: Contribution to journalArticlepeer-review

Abstract

We study addition operations between convex sets. We show that, under a short list of natural assumptions, one has polynomiality of volume only for the Minkowski addition. We also give two other characterization theorems. For the first theorem we define the induced homothety of an addition operation, and characterize additions by this homothety. The second theorem characterizes all additions which satisfy a short list of natural conditions.

Original languageEnglish
Article number1450022
JournalCommunications in Contemporary Mathematics
Volume17
Issue number3
DOIs
StatePublished - 25 Jun 2015

Keywords

  • Convex sets
  • Minkowski addition

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