We show that a if a Riemannian manifold admits a universal cover with bounded geometry and if 0 does not belong to the spectrum or is an isolated point in the spectrum of the Laplacian on $\ell$-forms, then there exists $1<p<2$ such that for all $p<r<p^{ \prime}$ the Hodge - de Rham decomposition for $L^{ r}$-forms holds ($p^{ \prime}$ denotes the conjugate of $p$).
Categories: math.SP math.DG