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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A generalization of outer parallel sets of a convex set


Author: J. R. Sangwine-Yager
Journal: Proc. Amer. Math. Soc. 123 (1995), 1559-1564
MSC: Primary 52A39; Secondary 52A40
MathSciNet review: 1233984
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Abstract: An outer parallel set is formed by adding outer normals of fixed length to the boundary points of a convex set. In this paper the length of the outer normals varies as a function of the direction. This construction yields a geometric interpretation of the dual quermassintegrals of Lutwak and bounds on certain mixed volumes. An inequality of Firey will follow from one of the mixed volume bounds.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1233984-0
PII: S 0002-9939(1995)1233984-0
Keywords: Brush set, mixed volume, outer parallel set, polar dual, quermassintegral
Article copyright: © Copyright 1995 American Mathematical Society