The theory of
compensated compactness of Murat and Tartar links the algebraic condition
of rank-r convexity with the analytic condition of weak
lower
semicontinuity. The former is an algebraic
condition and therefore it is, in principle, very easy to use. However,
in applications of this theory, the need for an efficient classification of
rank-r convex forms arises. In the present paper,
we define the concept of extremal 2-forms and characterize them
in the rotationally invariant jointly rank-r convex case.