  We obtain a volume growth and curvature decay result for various classes of
complete, noncompact Riemannian metrics in dimension 4; in particular our
method applies to anti-self-dual or Kahler metrics with zero scalar curvature,
and metrics with harmonic curvature. Similar results are known for Einstein
metrics, but our analysis differs from the Einstein case in that (1) we
consider more generally a fourth order system in the metric, and (2) we do not
assume any pointwise Ricci curvature bound.

Differential Geometry;Analysis of PDEs