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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
Posted:
September 30, 2011
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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
- 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), http://dx.doi.org/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
PII:
S 0002-9939(2011)11173-0
Received by editor(s):
February 2, 2011
Posted:
September 30, 2011
Communicated by:
Jianguo Cao
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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