Calculus of variations with differential forms
We study integrals of the form integral(Omega) f (d omega), where 1 <= k <= n, f : Lambda(k) -> R is continuous and omega is a (k - 1)-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 conclude with an application to a minimization problem.