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

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Convex Bodies of Constant Width,called convex bodies of constant width. Other names that have also been used are ‘convex bodies of constant breadth’, ‘equiwide convex bodies’, ‘orbiforms’ and ‘spheroforms’ (in the two and three-dimensional case, respectively) and several more; the occasionally used German ‘Gleichdick’ being one of the most charming.

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Convexity Through the Ages,s 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 endpoints, the length of the first arc is smaller than that of the second. The determination of surface areas is founded on an analogous postulate.

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Minimal and Closest Points Nonexpansive and Quasi-Nonexpansive Retractions in Real Banach Spaces,g among the above notions have not been considered in full. This present analysis shows that some results can be obtained from older ones, and other results can be restated in a sharper form using known facts and simple connections relating the various notions.

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Ellipsoids,wski geometries, Hilbert geometries, and affine differential geometry, ellipsoids play an important role. Known results on ellipsoids have been interpreted in the context of these geometries. On the other hand, problems formulated in these geometries have led to new results on ellipsoids.

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Technology, Mathematucs, and industry, convex bodies in spaces of constant curvature, i.e. in Euclidean, spherical and hyperbolic space. Instead of saying that . is a packing into the whole space or . is a covering of the whole space we shall simply use the terms . and ..

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Book 1983 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume ?Contributions to Geometry? edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the m

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