A Cheeger-like inequality for coexact 1-forms

Abstract

We state and prove a Cheeger-like inequality for coexact 1-forms on closed orientable Riemannian manifolds.

We corrected an error in Section 2 which changed the statement of our main theorem. In dimension 3 the result is the same that in the previous version but in dimension 4 and more the assumption that the Ricci curvature is bounded below has to be replaced with the assumption that the sectional curvature is bounded above and below