Journal of Convex Analysis, Vol. 7, No. 1, pp. 19-45 (2000)

Rank-One Connections at Infinity and Quasiconvex Hulls

Kewei Zhang

Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia,

Abstract: We define $p$-rank-one connections at infinity for an unbounded set $K$ in $M^{N\times n}$ and show that the quasiconvex hull $Q_p(K)$ may be bigger than $K$ if $K$ has a $p$-rank-one connection, where $Q_p(K)$ is the zero set of the quasiconvex relaxation of the $p$-distance function to $K$. We examine some examples and compare $Q_p(K)$ with $\mathbf{Q}_p(K)$ - a more restrictive quasiconvex hull of $K$.

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