
Journal of Convex Analysis 10 (2003), No. 2, 409417 Copyright Heldermann Verlag 2003 On the Equal Hull Problem for Nontrivial Semiconvex Hulls Kewei Zhang School of Mathematical Sciences, University of Sussex, Brighton BN1 9QH, United Kingdom, k.zhang@sussex.ac.uk [Abstractpdf] We define a nontrivial semiconvex hull $qr_{\alpha}(K)$ of a compact set $K\subset M^{N\times n}$ called the $\alpha$rankone convex quadratic hull and establish the equalities of semiconvex hulls with respect to $qr_{\alpha}(K)$ by showing that $L_c(K)=qr_{\alpha}(K)$ if and only if $Q(K)=qr_\alpha(K)$, 0 less than $\alpha$ less than 1, where $Q(K)$ and $L_c(K)$ are the quasiconvex convex hull and the closed lamination convex hull of $K$ respectively. We also show that $qr_{\alpha}(K)$ is a nontrivial semiconvex hull, that is, $qr_{\alpha}(K)\neq C(K)$ if $R(K)\neq C(K)$. FullTextpdf (306 K) 