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
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10.1512/iumj.2005.54.2665
10.1512/iumj.2005.54.2665
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Indiana Univ. Math. J. 54 (2005) 1483 - 1498
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