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

Vitali Milman, Liran Rotem

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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

Funding

FundersFunder number
United States-Israel Binational Science Foundation2012111
Israel Academy of Sciences and Humanities
Israel Science Foundation826/13

    Keywords

    • Convex sets
    • Minkowski addition

    Fingerprint

    Dive into the research topics of 'Characterizing addition of convex sets by polynomiality of volume and by the homothety operation'. Together they form a unique fingerprint.

    Cite this