Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 351361 (2006) 

Addition and subtraction of homothety classes of convex setsValeriu SoltanDepartment of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030, USA, email: vsoltan@gmu.eduAbstract: Let $S_H$ denote the homothety class generated by a convex set $S \subset {\mathbb R}^n$: $S_H = \{a + \lambda S \mid a \in {\mathbb R}^n, \lambda > 0\}$. We determine conditions for the Minkowski sum $B_H + C_H$ or the Minkowski difference $B_H \sim C_H$ of homothety classes $B_H$ and $C_H$ generated by closed convex sets $B,C \subset {\mathbb R}^n$ to lie in a homothety class generated by a closed convex set (more generally, in the union of countably many homothety classes generated by closed convex sets). Keywords: convex set, homothety class, Minkowski sum, Minkowski difference Classification (MSC2000): 52A20 Full text of the article:
Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.
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