On the weighted forward reduced volume of Ricci flow
Authors:
Liang Cheng and Anqiang Zhu
Journal:
Proc. Amer. Math. Soc. 141 (2013), 28592868
MSC (2010):
Primary 53C44
Published electronically:
April 9, 2013
MathSciNet review:
3056576
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Abstract 
References 
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Additional Information
Abstract: In this paper, we introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which is related to expanders of Ricci flow, is welldefined on noncompact manifolds and monotone nonincreasing under Ricci flow. Moreover, we show that, just the same as Perelman's reduced volume, the weighted reduced volume entropy has the value if and only if the Ricci flow is the trivial flow on flat Euclidean space.
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 J. Enders, R. Müller, P. M. Topping, On Type I singularities in Ricci flow, Comm. Anal. Geom. 19 (2011), no. 5, 905922. MR 2886712
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 M. Feldman, T. Ilmanen, L. Ni, Entropy and reduced distance for Ricci expanders, J. Geom. Anal. 15 (2005), 4962. MR 2132265 (2006b:53091)
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 Kotschwar, Brett L. Backwards uniqueness for the Ricci flow. Int. Math. Res. Not. IMRN (2010), no. 21, 40644097. MR 2738351 (2012c:53100)
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/math/0303109v1.
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Additional Information
Liang Cheng
Affiliation:
School of Mathematics and Statistics, Huazhong Normal University, Wuhan, 430079, People’s Republic of China
Email:
math.chengliang@gmail.com
Anqiang Zhu
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China
Email:
anqiangzhu@yahoo.com.cn
DOI:
http://dx.doi.org/10.1090/S000299392013116874
Keywords:
Ricci flow,
weighted forward reduced volume,
Type III singularities,
gradient expanding soliton
Received by editor(s):
October 31, 2011
Published electronically:
April 9, 2013
Additional Notes:
The first author was supported by NSF grant of China No. 11171126 and selfdetermined research funds of CCNU from the colleges basic research and operation of MOE CCNU11A01027
The second author was supported by NSF grant of China No. 11126190
Communicated by:
Lei Ni
Article copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
