no. 23-24
Differential Geometry
Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons
[Minorer des la courbures scalaires de solitons de Ricci gradient non compact]

Présenté par : Jean-Pierre Demailly

Chow, Bennett1 ; Lu, Peng2 ; Yang, Bo1
1 Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, United States
2 Department of Mathematics, University of Oregon, Eugene, OR 97403, United States
Comptes Rendus. Mathématique, Tome 349 (2011) no. 23-24, pp. 1265-1267.

Nous montrons que les travaux récents de Ni et Wilking (in preparation) [11] donne le résultat dʼun non plate soliton contractant de type gradient non compact a tout au plus sa courbure scalaire avec décroissance quadratique. Les exemples de solitons de Kähler–Ricci contractant de type non compact par Feldman, Ilmanen, et Knopf (2003) [7] montre que ce résultat est optimales. Nous prouvons aussi un résultat similaire pour certains solitons de Ricci stable de type gradient non compact.

We show that recent work of Ni and Wilking (in preparation) [11] yields the result that a noncompact nonflat Ricci shrinker has at most quadratic scalar curvature decay. The examples of noncompact Kähler–Ricci shrinkers by Feldman, Ilmanen, and Knopf (2003) [7] exhibit that this result is sharp. We also prove a similar result for certain noncompact steady gradient Ricci solitons.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.11.004
Chow, Bennett 1 ; Lu, Peng 2 ; Yang, Bo 1

1 Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, United States
2 Department of Mathematics, University of Oregon, Eugene, OR 97403, United States 
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Chow, Bennett; Lu, Peng; Yang, Bo. Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons. Comptes Rendus. Mathématique, Tome 349 (2011) no. 23-24, pp. 1265-1267. doi : 10.1016/j.crma.2011.11.004. http://www.numdam.org/articles/10.1016/j.crma.2011.11.004/

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