Novel view on classical convexity theory

Vitali Milman; Liran Rotem

doi:https://doi.org/10.15407/mag16.03.291

Novel view on classical convexity theory

Vitali Milman, Liran Rotem

Tel Aviv University, Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Let B_x ⊆ 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 language	English
Pages (from-to)	291-311
Number of pages	21
Journal	Journal of Mathematical Physics, Analysis, Geometry
Volume	16
Issue number	3
DOIs	https://doi.org/10.15407/mag16.03.291
State	Published - 2020

Keywords

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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https://doi.org/10.15407/mag16.03.291

Cite this

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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",

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year = "2020",

doi = "https://doi.org/10.15407/mag16.03.291",

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AU - Rotem, Liran

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PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Convex bodies

KW - Duality

KW - Dvoretzky’s Theorem

KW - Flowers

KW - Powers

KW - Spherical inversion

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DO - https://doi.org/10.15407/mag16.03.291

M3 - مقالة

SN - 1812-9471

VL - 16

SP - 291

EP - 311

JO - Journal of Mathematical Physics, Analysis, Geometry

JF - Journal of Mathematical Physics, Analysis, Geometry

IS - 3

ER -

Novel view on classical convexity theory

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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