Quasiconvexity equals lamination convexity for isotropic sets of \(2\times2\) matrices (Q486467)

The main result of this paper states that the quasiconvex hull of a compact isotropic set of real \(2\times 2\) matrices coincides with its lamination convex hull of order 2, generalizing the statement from [\textit{S. Conti} et al., C. R., Math., Acad. Sci. Paris 337, No. 4, 233--238 (2003; Zbl 1050.49010)] where the set is taken to be also connected. A direct consequence of this assertion is that for such sets the notions of quasiconvexity, rank-one convexity and lamination convexity are equivalent. Several lemmata used to prove the main statement are also worth mentioning, as they generalize assertions from the literature.