On the weighted forward reduced volume of Ricci flow

Authors:
Liang Cheng and Anqiang Zhu

Journal:
Proc. Amer. Math. Soc. **141** (2013), 2859-2868

MSC (2010):
Primary 53C44

Published electronically:
April 9, 2013

MathSciNet review:
3056576

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Abstract | References | Similar Articles | 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 well-defined 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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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:
https://doi.org/10.1090/S0002-9939-2013-11687-4

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 self-determined 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.