  Weighted quadratic estimates are proved for certain bisectorial firstorder
differential operators with bounded measurable coefficients which are (not
necessarily pointwise) accretive, on complete manifolds with positive
injectivity radius. As compared to earlier results, Ricci curvature is only
assumed to be bounded from below, and the weight is only assumed to be locally
in A^2. The Kato square root estimate is proved under this weaker assumption.
On compact Lipschitz manifolds we prove solvability estimates for solutions to
degenerate elliptic systems with not necessarily self-adjoint coefficients, and
with Dirichlet, Neumann and Atiyah-Patodi-Singer boundary conditions.
