Titlebook: Convexity and Its Applications; Peter M. Gruber,Jörg M. Wills Book 1983 Springer Basel AG 1983 optimization.research.science and technolog

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Algebraic Lattices,kerkerker [6]. As none of these sources deals specifically with lattices other than those of Minkowski-type (i.e. a ℤ-module with N generators in ℝ.) it seems worthwhile to trace the main developments there for lattices which have more algebraic structure. Even though these are often endowed with ar

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Convexity Through the Ages, and all chords of which lie on the same side of it. Analogously he defines a convex surface bounded by a plane curve. His determination of arc lengths is based on certain postulates. One of these is: If one of two convex arcs with common endpoints lies between the other and the line joining the end

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Approximation of convex bodies,t. On the one hand approximation is used as a tool for investigations ranging from classical results on mixed volumes to questions concerning the ε-entropy of spaces of convex bodies, on the other hand there is an intrinsic geometric interest in the approximation problem itself.

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Valuations on convex bodies, of geometric convexity, and it has seen some progress in recent years. The occurrence of valuations in the theory of convex bodies can be traced back to the notion of volume in two essentially different ways. Firstly, the volume of convex bodies, being the restriction of a measure, is itself a valu