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Journal of Convex Analysis 07 (2000), No. 1, 019--046
Copyright Heldermann Verlag 2000

Rank-One Connections at Infinity and Quasiconvex Hulls

Kewei Zhang
Dept. of Mathematics, Macquarie University, Sydney, NSW 2109, Australia

We define p-rank-one connections at infinity for an unbounded set K in MN×n and show that the quasiconvex hull Qp(K) may be bigger than K if K has a p-rank-one connection, where Qp(K) is the zero set of the quasiconvex relaxation of the p-distance function to K. We examine some examples and compare Qp(K) with Qp(K) - a more restrictive quasiconvex hull of K.

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