  We study critical Riemannian 4-manifolds with a lower bound on Ricci
curvature, but no a priori analytic constraints such as on Sobolev constants.
We derive elliptic-type estimates for the local curvature radius, which itself
controls sectional curvature. The primary method is construction of blow-ups of
degenerating metrics, followed by a geometric/topological triviality result
from a previous work.
