Anti-self-duality of curvature and degeneration of metrics with special holonomy

Jeff Cheeger, Gang Tian

Research output: Contribution to journalArticlepeer-review


We study the structure of noncollapsed Gromov-Hausdorff limits of sequences, Min, of riemannian manifolds with special holonomy. We show that these spaces are smooth manifolds with special holonomy off a closed subset of codimension ≥4. Additional results on the the detailed structure of the singular set support our main conjecture that if the M in are compact and a certain characteristic number, C(Min), is bounded independent of i, then the singularities are of orbifold type off a subset of real codimension at least 6.

Original languageEnglish (US)
Pages (from-to)391-417
Number of pages27
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Apr 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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