@article{2596358ad683446a9d1f9c1c9da11b60,

title = "Novel view on classical convexity theory",

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.",

keywords = "Convex bodies, Duality, Dvoretzky{\textquoteright}s Theorem, Flowers, Powers, Spherical inversion",

author = "Vitali Milman and Liran Rotem",

note = "Publisher Copyright: {\textcopyright} Vitali Milman and Liran Rotem, 2020.",

year = "2020",

doi = "10.15407/mag16.03.291",

language = "אנגלית",

volume = "16",

pages = "291--311",

journal = "Journal of Mathematical Physics, Analysis, Geometry",

issn = "1812-9471",

publisher = "ILTPE-B. Verkin Institute for Low Temperature Physics and Engineering",

number = "3",

}