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We consider the L_{q,p}-cohomology of a complete simply connected Riemannian manifold (M,g) with pinched negative curvature. The connection between the L_{q,p}-cohomology of (M,g) and Sobolev inequalities for differential forms on (M,g) was established by the authors in a previous publications.

L q,p -Cohomology of Riemannian Manifolds with Negative Curvature