Isoperimetric type inequalities for differential forms on manifolds Flavia GiannettiAntonia Passarelli di Napoli Let $X$ be a smooth oriented Riemannian $n$-manifold without boundary and $(\Phi,\Psi) \in \mathcal{L}^p(\bigwedge^{\ell}X) \times \mathcal{L}^r(\bigwedge^{n-\ell}X)$, $1/p + 1/r = 1 + 1/n$, be a pair of closed differential forms. We prove an isoperimetric type inequality for such differential forms under suitable assumptions. As an application we derive H\"older continuity for solutions of Hodge systems. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2665 10.1512/iumj.2005.54.2665 en Indiana Univ. Math. J. 54 (2005) 1483 - 1498 state-of-the-art mathematics http://iumj.org/access/