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

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

2005-06-03

arxiv.org/abs/math/0506065v6

J. Geom. Anal. 16 (2006), no. 4, 597--631

Mathematics

Differential Geometry

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

Scientific paper

10.1007/BF02922133

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 $L^q(M)$.

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