Bach-flat asymptotically locally Euclidean metrics

Gang Tian, Jeff Viaclovsky

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


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 Kähler metrics with zero scalar curvature, and metrics with harmonic curvature. Similar results were obtained for Einstein metrics in [And89], [BKN89], [Tia90], 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.

Original languageEnglish (US)
Pages (from-to)357-415
Number of pages59
JournalInventiones Mathematicae
Issue number2
StatePublished - May 2005

All Science Journal Classification (ASJC) codes

  • General Mathematics


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