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Polar Means of Convex Bodies and a Dual to the Brunn-Minkowski Theorem

Published online by Cambridge University Press:  20 November 2018

William J. Firey
William J. Firey*
Affiliation:
Washington State University
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This paper deals with processes of combining convex bodies in Euclidean n-space which are, in a sense, dual to the process of Minkowski addition and some of its generalizations.

All the convex bodies considered will have a common interior point Q. Variables x and y denote vectors drawn from Q; we shall speak of their terminal points as the points x and y. Unit vectors will be denoted by u; ||x|| signifies the length of x. Convex bodies will be symbolized by K with distinguishing marks. ∂K means the boundary of K. λK will mean the image of K under a homothetic transformation in the ratio λ : 1. The centre of the homothety will always be Q.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 444 - 453
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Bonnesen, T. and Fenchel, W., Théorie der Konvexen Kôrper (New York, 1948).Google Scholar
2. Firey, W., p-Means of convex bodies, submitted to Math. Scand. (Oct., 1959).Google Scholar