Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay

Chow, Bennett; Lu, Peng

doi:10.1016/j.crma.2015.09.009

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

Chow, Bennett ¹ ; Lu, Peng 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

Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 1007-1009.

Résumé
Abstract

Nous montrons que tout soliton gradient de Ricci contractant complet non compact vérifiant la propriété (1) $| Rc | \to 0$ à l'infini ou (2) $R \to 0$ 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) $| Rc | \to 0$ at infinity or (2) $R \to 0$ at infinity, $| Rm |$ bounded, and κ-noncollapsed has a unique asymptotic cone.

Reçu le : 2015-07-15
Accepté le : 2015-09-14
Publié le : 2015-10-23

DOI : 10.1016/j.crma.2015.09.009

Affiliations des auteurs :

Chow, Bennett ¹ ; Lu, Peng 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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     title = {Uniqueness of asymptotic cones of complete noncompact shrinking gradient {Ricci} solitons with {Ricci} curvature decay},
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Chow, Bennett; Lu, Peng. Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 1007-1009. doi : 10.1016/j.crma.2015.09.009. http://www.numdam.org/articles/10.1016/j.crma.2015.09.009/

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