Gol'dshtein, VladimirTroyanov, Marc2007-12-172007-12-172007-12-17200610.1007/BF02922133https://infoscience.epfl.ch/handle/20.500.14299/15785WOS:0002424770000049666We 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 $L^q(M)$.text::journal::journal article::research article