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Area growth rate of the level surface of the potential function on the 3-dimensional steady gradient Ricci soliton
Author(s):
Hongxin
Guo
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2093-2097.
MSC (2000):
Primary 53C44
Posted:
January 29, 2009
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Abstract:
In this short note we show that on a 3-dimensional steady gradient Ricci soliton with positive curvature and which is  -noncollapsed on all scales, the scalar curvature and the mean curvature of the level surface of the potential function both decay linearly. Consequently we prove that the area of the level surface grows linearly.
References:
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Additional Information:
Hongxin
Guo
Affiliation:
School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, 325035 People's Republic of China
Email:
hguo2006@gmail.com
DOI:
10.1090/S0002-9939-09-09792-5
PII:
S 0002-9939(09)09792-5
Received by editor(s):
May 30, 2008,
Received by editor(s) in revised form:
September 26, 2008
Posted:
January 29, 2009
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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