Sobolev Inequalities for Differential Forms and $L_{q,p}$-cohomology

Abstract

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is defined to be the quotient of the space of closed differential forms in $L^p(M)$ modulo the exact forms which are exterior differentials of forms in $L^q(M)$.

This paper has appeared in the Journal of Geometric Analysis, (only minor changes have been made since verion 1)

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