On the composition of quasiconvex functions and the transposition

If G : R-nxm -> (R) over bar := R boolean OR {+infinity} is a convex, polyconvex or rank-one convex function, then the function g : R-mxn -> (R) over bar defined as g(A) = G(A(t)) preserves convexity, polyconvexity, or rank-one convexity, respectively. The paper shows that this does not hold in general for quasiconvexity provided n >= 2 and m >= 3.