Geodesic
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.

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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.

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.

Reçu le :
Accepté le :
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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://geodesic.mathdoc.fr/articles/10.1016/j.crma.2011.11.004/

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