Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons

Bennett Chow; Peng Lu; Bo Yang

doi:10.1016/j.crma.2011.11.004

Differential Geometry

Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons

Presented by: Jean-Pierre Demailly

Bennett Chow ¹; Peng Lu ²; Bo Yang 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

Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1265-1267.

Abstract
Résumé

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.

Received: 2011-03-11
Accepted: 2011-11-04
Published online: 2011-11-16

DOI: 10.1016/j.crma.2011.11.004

Author's affiliations:

Bennett Chow ¹; Peng Lu ²; Bo Yang 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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     title = {Lower bounds for the scalar curvatures of noncompact gradient {Ricci} solitons},
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Bennett Chow; Peng Lu; Bo Yang. Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons. Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1265-1267. doi : 10.1016/j.crma.2011.11.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.11.004/

References
Cited by

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