Title: Isoperimetric type inequalities for differential forms on manifolds

Authors: Flavia Giannetti and Antonia Passarelli di Napoli

Issue: Volume 54 (2005), Issue 5, 1483-1498

Abstract: 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.