On a conformal gap and finiteness theorem for a class of four-manifolds

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In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and make a comparison of the solutions of the σ k equations on a degenerating family of Bach-flat metrics.

Original languageEnglish (US)
Pages (from-to)404-434
Number of pages31
JournalGeometric and Functional Analysis
Issue number2
StatePublished - Jun 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


  • Bach-flat metrics
  • Bubble-tree structure
  • Curvature concentrations
  • Finite diffeomorphism theorem
  • Gap theorem
  • Neck theorem


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