Distances on Convex Bodies, Cones, and Simplicial Complexes

Michel Marie Deza and Elena Deza
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Michel Marie Deza: Ecole Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 9 in Encyclopedia of Distances, 2016, pp 183-195 from Springer

Abstract: Abstract A convex body in the n-dimensional Euclidean space $$\mathbb{E}^{n}$$ is a convex compact connected subset of $$\mathbb{E}^{n}$$ . It is called solid (or proper) if it has nonempty interior. Let K denote the space of all convex bodies in $$\mathbb{E}^{n}$$ , and let K p be the subspace of all proper convex bodies. Given a set $$X \subset \mathbb{E}^{n}$$ , its convex hull c o n v(X) is the minimal convex set containing X.

Keywords: Convex Body; Simplicial Complex; Convex Cone; Jordan Algebra; Symmetric Cone (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-662-52844-0_9

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