Novel view on classical convexity theory

Vitali Milman, Liran Rotem

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - 2020


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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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