Comptes Rendus
no. 11
Differential geometry
Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay
[Unicité des cônes asymptotiques des solitons gradients de Ricci contractants complets non compacts avec courbure de Ricci décroissante]

Présenté par : Étienne Ghys

Bennett Chow1 ; Peng Lu2
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, Volume 353 (2015) no. 11, pp. 1007-1009.

Nous montrons que tout soliton gradient de Ricci contractant complet non compact vérifiant la propriété (1) |Rc|→0 à l'infini ou (2) R→0 à l'infini, avec |Rm| bornée et κ-non-effrondée, possède un cône asymptotique unique.

We show that any complete noncompact shrinking gradient Ricci soliton with (1) |Rc|→0 at infinity or (2) R→0 at infinity, |Rm| bounded, and κ-noncollapsed has a unique asymptotic cone.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.009
Bennett Chow 1 ; Peng Lu 2

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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Bennett Chow; Peng Lu. Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1007-1009. doi : 10.1016/j.crma.2015.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.009/

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