Novel view on classical convexity theory

Vitali Milman, Liran Rotem

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let Bx ⊆ Rn denote the Euclidean ball with diameter [0, x], i.e., with with center at x/2 and radius x/2. We call such a ball a petal. A flower F is any union of petals, i.e., (formula presented) for any set A ⊆ Rn. We showed earlier in [9] that the family of all flowers F is in 1-1 correspondence with K0 – the family of all convex bodies containing 0. Actually, there are two essentially different such correspondences. We demonstrate a number of different nonlinear constructions on F and K0. Towards this goal we further develop the theory of flowers.

Original languageEnglish
Pages (from-to)291-311
Number of pages21
JournalJournal of Mathematical Physics, Analysis, Geometry
Volume16
Issue number3
DOIs
StatePublished - 2020

Funding

FundersFunder number
United States-Israel Binational Science Foundation
Israel Science Foundation1468/19, 519/17

    Keywords

    • Convex bodies
    • Duality
    • Dvoretzky’s Theorem
    • Flowers
    • Powers
    • Spherical inversion

    Fingerprint

    Dive into the research topics of 'Novel view on classical convexity theory'. Together they form a unique fingerprint.

    Cite this