Hodge decomposition of the Sobolev space $H^1$ on a space form of nonpositive curvature

Chi Hin Chan, Magdalena Czubak, Carlos Pinilla Suarez

The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to include non-compact manifolds and $L^2$ forms. We further extend the Hodge d…