Let $m,n\in\mathbb N$, set $r:=\min\{m,n\}$, and for each $1\le k\le r$ let $\mathcal I_k$ and $\mathcal J_k$ be the sets of strictly increasing $k$-tuples of row indices in $\{1,\dots,m\}$ and column indices in $\{1,\dots,n\}$, respectively. For $A\in\mathbb R^{m\times n}$ and $(I,J)\in\mathcal I_k\times\mathcal J_k$, let $A_{I,J}\in\mathbb R^{k\times k}$ denote the corresponding submatrix, and define the full minors map $M:\mathbb R^{m\times n}\to\mathbb R^N$ by listing all numbers $\det A_{I,J}$ for $1\le k\le r$, where $N:=\sum_{k=1}^r \#\mathcal I_k\,\#\mathcal J_k$. Suppose $W:\mathbb R^{m\times n}\to\mathbb R$ is finite and polyconvex, meaning that there exists a finite [convex function](/page/Convex%20Function) $G:\mathbb R^N\to\mathbb R$ such that $W(A)=G(M(A))$ for every $A\in\mathbb R^{m\times n}$. Then $W$ is quasiconvex: for every bounded [open set](/page/Open%20Set) $V\subset\mathbb R^n$ with $\mathcal L^n(V)>0$, every $A\in\mathbb R^{m\times n}$, and every $\varphi\in W^{1,\infty}_0(V;\mathbb R^m)$, one has

\begin{align*} W(A)\le \frac{1}{\mathcal L^n(V)}\int_V W(A+\nabla\varphi(x))\,d\mathcal L^n(x). \end{align*}