Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia, kewei@ics.mq.edu.au
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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