Moduli spaces of critical Riemannian metrics in dimension four

Gang Tian, Jeff Viaclovsky

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kähler metrics with constant scalar curvature, and metrics with harmonic curvature. With certain geometric non-collapsing assumptions, the moduli space can be compactified by adding metrics with orbifold-like singularities. Similar results were obtained for Einstein metrics in (J. Amer. Math. Soc. 2(3) (1989) 455, Invent. Math. 97 (2) (1989) 313, Invent. Math. 101(1) (1990) 101), but our analysis differs substantially from the Einstein case in that we do not assume any pointwise Ricci curvature bound.

Original languageEnglish (US)
Pages (from-to)346-372
Number of pages27
JournalAdvances in Mathematics
Issue number2
StatePublished - Oct 1 2005

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Anti-self-dual metrics
  • Orbifolds


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