On the \(L^p\) independence of the spectrum of the Hodge Laplacian on non-compact manifolds (Q557034)

The spectrum of the Hodge Laplacian acting on \(L^p\)-differential forms of order \(k\) is considered on open manifolds whose Ricci curvature is bounded from below and whose volume growth is uniformly subexponential. It is shown that for \(1\leq p \leq \infty\) the \(L^p\)-spectrum of the Hodge Laplacian is independent of \(p\) if the Weitzenböck tensor on \(k\)-forms is also bounded from below. As a consequence the author shows that the spectrum of the Laplacian on one-forms has no gaps for example on certain warped products.