Jiu-Yuan Cui

On the space of harmonic forms and Schr\"odinger heat equations on noncompact manifolds

It is known that on complete Riemannian manifolds with nonnegative Ricci curvature, the space of harmonic 1-forms of polynomial growth is finite-dimensional. In this paper, we extend this finiteness phenomenon to some manifolds whose Ricci curvature is allowed to be negative. More precisely, under a scale-invariant $L^...