Area growth rate of the level surface of the potential function on the 3-dimensional steady gradient Ricci soliton
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- by Hongxin Guo PDF
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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.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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2093-2097
- MSC (2000): Primary 53C44
- DOI: https://doi.org/10.1090/S0002-9939-09-09792-5
- MathSciNet review: 2480291