A generalization of outer parallel sets of a convex set

Sangwine-Yager, J. R.

doi:10.1090/S0002-9939-1995-1233984-0

A generalization of outer parallel sets of a convex set
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by J. R. Sangwine-Yager PDF

Proc. Amer. Math. Soc. 123 (1995), 1559-1564 Request permission

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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