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Area growth rate of the level surface of the potential function on the 3-dimensional steady gradient Ricci soliton

Author: Hongxin Guo
Journal: Proc. Amer. Math. Soc. 137 (2009), 2093-2097
MSC (2000): Primary 53C44
Published electronically: January 29, 2009
MathSciNet review: 2480291
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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 $ \kappa$-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.

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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

Received by editor(s): May 30, 2008
Received by editor(s) in revised form: September 26, 2008
Published electronically: January 29, 2009
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.