  In this short note, we provide a quantitative global Poincar\'e inequality
for one forms on a closed Riemannian four manifold, in terms of an upper bound
on the diameter, a positive lower bound on the volume, and a two-sided bound on
Ricci curvature. This seems to be the first non-trivial result giving such an
inequality without any higher curvature assumptions. The proof is based on a
Hodge theoretic result on orbifolds, a comparison for fundamental groups, and a
spectral convergence with respect to Gromov-Hausdorff convergence, via a
degeneration result to orbifolds by Anderson.
