Quasiconvexity is not invariant under transposition

An example is given of a quasiconvex f : M-2x3 --> R such that the transposed function (f) over tilde : M-3x2 --> R given by (f) over tilde(F) = f(F-T) is not quasiconvex. For (f) over tilde one can take Sverak's quartic polynomial that is rank-one convex but not quasiconvex. The proof is closely related to the observation that the map v bar right arrow v(1)v(2)v(3) is weakly continuous from L-3(R-3;R-3) into distributions provided that A(Dv) = (partial derivative(2)v(1), partial derivative(3)v(1), partial derivative(1)v(2), partial derivative(3)v(2), partial derivative(1)v(3), partial derivative(2)v(3)) is compact in W--1,W-3(R-3;R-6).