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Convex bodies of constant outer p-measure

Published online by Cambridge University Press:  26 February 2010

William J. Firey
William J. Firey
Affiliation:
Oregon State University, Corvallis, Oregon, U.S.A.
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Extract

Suppose K is a convex body in Euclidean n-space En and that all the orthogonal projections of K onto p-dimensional linear subspaces have the same p-dimensional volume, that is K has constant outer p-measure. If p = 1, this means that K is of constant width; if p = n − 1, this means that K has constant brightness. It is known that, when the boundary of K is smooth enough to admit principal radii of curvature R1, …, Rn-1 as functions of the outer normal u, and if we define Fp(u) to be the p-th elementary symmetric function of these radii, then, when K has constant width,

Type
Research Article
Information
Mathematika , Volume 17 , Issue 1 , June 1970 , pp. 21 - 27
Copyright
Copyright © University College London 1970

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References

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