Bachflat asymptotically locally Euclidean metrics
Abstract
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 antiselfdual 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.
 Publication:

Inventiones Mathematicae
 Pub Date:
 December 2004
 DOI:
 10.1007/s0022200404121
 arXiv:
 arXiv:math/0310302
 Bibcode:
 2004InMat.160..357T
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 53C25;
 58E11;
 53C21
 EPrint:
 54 pages