[Bornes Lp sur la courbure, estimées elliptiques et rectifiabilité d'ensembles singuliers]
Nous annonçons des résultats de rectifiabilité des ensembles singuliers dans les espaces métriques pointés qui sont des limites au sens de Gromov–Hausdorff d'une suite de variétés riemanniennes pour lesquelles on a une borne uniforme sur la courbure de Ricci, le volume, et des bornes uniformes Lp sur la courbure. Les théorèmes de rectifiabilité dépendent d'estimations sur |Hessh|L2p, (|∇Hessh·|Hessh|p−2)L2, où Δh=c, pour une constante c. Nous remarquons également que dans le cas Kählérien (en l'absence de toute borne intégrale sur la courbure), l'ensemble singulier est de codimension complexe 2.
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.
Publié le :
@article{CRMATH_2002__334_3_195_0,
author = {Cheeger, Jeff},
title = {\protect\emph{L}\protect\textsubscript{\protect\emph{p}}-bounds on curvature, elliptic estimates and rectifiability of singular sets},
journal = {Comptes Rendus. Math\'ematique},
pages = {195--198},
publisher = {Elsevier},
volume = {334},
number = {3},
year = {2002},
doi = {10.1016/S1631-073X(02)02238-0},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02238-0/}
}
TY - JOUR AU - Cheeger, Jeff TI - Lp-bounds on curvature, elliptic estimates and rectifiability of singular sets JO - Comptes Rendus. Mathématique PY - 2002 SP - 195 EP - 198 VL - 334 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02238-0/ DO - 10.1016/S1631-073X(02)02238-0 LA - en ID - CRMATH_2002__334_3_195_0 ER -
%0 Journal Article %A Cheeger, Jeff %T Lp-bounds on curvature, elliptic estimates and rectifiability of singular sets %J Comptes Rendus. Mathématique %D 2002 %P 195-198 %V 334 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02238-0/ %R 10.1016/S1631-073X(02)02238-0 %G en %F CRMATH_2002__334_3_195_0
Cheeger, Jeff. Lp-bounds on curvature, elliptic estimates and rectifiability of singular sets. Comptes Rendus. Mathématique, Tome 334 (2002) no. 3, pp. 195-198. doi : 10.1016/S1631-073X(02)02238-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)02238-0/
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