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This article is cited in 2 scientific papers (total in 2 papers)
Novel view on classical convexity theory
Vitali Milmana, Liran Rotemb a Tel Aviv University, Tel-Aviv, 69978, Israel
b Technion – Israel Institute of Technology, Haifa, 32000, Israel
Abstract:
Let $B_{x}\subseteq\mathbb{R}^{n}$ denote the Euclidean ball with diameter $[0,x]$, i.e., with center at $\frac{x}{2}$ and radius $\frac{\left|x\right|}{2}$. We call such a ball a petal. A flower $F$ is any union of petals, i.e., $F=\bigcup_{x\in A}B_{x}$ for any set $A\subseteq\mathbb{R}^{n}$. We showed earlier in [9] that the family of all flowers $\mathcal{F}$ is in 1-1 correspondence with $\mathcal{K}_{0}$ – the family of all convex bodies containing $0$. Actually, there are two essentially different such correspondences. We demonstrate a number of different non-linear constructions on $\mathcal{F}$ and $\mathcal{K}_{0}$. Towards this goal we further develop the theory of flowers.
Key words and phrases:
convex bodies, flowers, spherical inversion, duality, powers, Dvoretzky's Theorem.
Received: 28.04.2020
Citation:
Vitali Milman, Liran Rotem, “Novel view on classical convexity theory”, Zh. Mat. Fiz. Anal. Geom., 16:3 (2020), 291–311
Linking options:
https://www.mathnet.ru/eng/jmag759 https://www.mathnet.ru/eng/jmag/v16/i3/p291
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Abstract page: | 86 | Full-text PDF : | 60 | References: | 10 |
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