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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

A necessary and sufficient condition for Ricci shrinkers to have positive AVR


Authors: Bennett Chow, Peng Lu and Bo Yang
Journal: Proc. Amer. Math. Soc. 140 (2012), 2179-2181
MSC (2010): Primary 53Cxx
Published electronically: September 30, 2011
MathSciNet review: 2888203
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Abstract: In this short paper we observe that a recent result of C.-W. Chen meshes well with earlier work of H.-D. Cao and D.-T. Zhou, O. Munteanu, J. Carrillo and L. Ni, and S.-J. Zhang. We give a necessary and sufficient condition for complete noncompact shrinking gradient Ricci solitons to have positive asymptotic volume ratio.


References [Enhancements On Off] (What's this?)

  • 1. Huai-Dong Cao and Detang Zhou, On complete gradient shrinking Ricci solitons, J. Differential Geom. 85 (2010), no. 2, 175–185. MR 2732975 (2011k:53040)
  • 2. Carrillo, José A., Ni, Lei, Sharp logarithmic Sobolev inequalities on gradient solitons and applications. Communications in Analysis and Geometry 17 (2009), 721-753.
  • 3. Bing-Long Chen, Strong uniqueness of the Ricci flow, J. Differential Geom. 82 (2009), no. 2, 363–382. MR 2520796 (2010h:53095)
  • 4. Chen, Chih-Wei, On the injectivity radius and tangent cones at infinity of gradient Ricci solitons. arXiv:1012.1217.
  • 5. Fu-quan Fang, Jian-wen Man, and Zhen-lei Zhang, Complete gradient shrinking Ricci solitons have finite topological type, C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 653–656 (English, with English and French summaries). MR 2423272 (2009e:53043), 10.1016/j.crma.2008.03.021
  • 6. Haslhofer, Robert, Müller, Reto, A compactness theorem for complete Ricci shrinkers. arXiv:1005.3255v2.
  • 7. Munteanu, Ovidiu, The volume growth of complete gradient shrinking Ricci solitons. arXiv:0904.0798.
  • 8. Zhang, Shijin. On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below. arXiv:0909.0716, Acta Mathematica Sinica 27, no. 5 (2011), 871-882.

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Additional Information

Bennett Chow
Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
Email: benchow@math.ucsd.edu

Peng Lu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: penglu@uoregon.edu

Bo Yang
Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
Email: b5yang@math.ucsd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11173-0
Received by editor(s): February 2, 2011
Published electronically: September 30, 2011
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.