Lp-bounds on curvature, elliptic estimates and rectifiability of singular sets

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Abstract

We announce results on rectifiability of singular sets of pointed metric spaces which are pointed Gromov-Hausdorff limits on sequences of Riemannian manifolds, satisfying uniform lower bounds on Ricci curvature and volume, and uniform Lp-bounds on curvature. The rectifiability theorems depend on estimates for Hessh L2p, ( ∇Hessh. Hessh p-2)L2, where Δh = c, for some constant c. We also observe that (absent any integral bound on curvature) in the Kähler case, given a uniform 2-sided bound on Ricci curvature, the singular set has complex codimension 2.

Original languageEnglish (US)
Pages (from-to)195-198
Number of pages4
JournalComptes Rendus Mathematique
Volume334
Issue number3
DOIs
StatePublished - Feb 15 2002

ASJC Scopus subject areas

  • Mathematics(all)

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