  We study integrals of the form $\int_{\Omega}f\left( d\omega\right)$, where
$1\leq k\leq n$, $f:\Lambda^{k}\rightarrow\mathbb{R}$ is continuous and
$\omega$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of
convexity, namely ext. one convexity, ext. quasiconvexity and ext.
polyconvexity. We study their relations, give several examples and
counterexamples. We finally conclude with an application to a minimization
problem.
