Abstract
We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the Lq,p-cohomology of that manifold.
The Lq,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in Lp(M) modulo the exact forms which are exterior differentials of forms in Lq (M).
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Gol’dshtein, V., Troyanov, M. Sobolev inequalities for differential forms andL q,p -cohomology. J Geom Anal 16, 597–631 (2006). https://doi.org/10.1007/BF02922133
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DOI: https://doi.org/10.1007/BF02922133