Structure theory and convergence in Riemannian geometry

Research output: Contribution to journalArticlepeer-review


We sketch a sequence of developments in riemannian geometry which have taken place over roughly the last 50 years. These concern structure theories for manifolds satisfying bounds on sectional or Ricci curvature, and related theories of geometric convergence. As an illustration, we describe some applications to the study of Einstein metrics in dimension 4.

Original languageEnglish (US)
Pages (from-to)221-264
Number of pages44
JournalMilan Journal of Mathematics
Issue number1
StatePublished - 2010


  • Collapsing
  • Convergence
  • Einstein metric
  • Ricci curvature
  • Riemannian geometry
  • Rigidity
  • Sectional curvature

ASJC Scopus subject areas

  • General Mathematics


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