TY - JOUR
T1 - Lp-bounds on curvature, elliptic estimates and rectifiability of singular sets
AU - Cheeger, Jeff
PY - 2002/2/15
Y1 - 2002/2/15
N2 - 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.
AB - 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.
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U2 - 10.1016/S1631-073X(02)02238-0
DO - 10.1016/S1631-073X(02)02238-0
M3 - Article
AN - SCOPUS:0011686449
SN - 1631-073X
VL - 334
SP - 195
EP - 198
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 3
ER -