The second variational formula for the functional $\int v^{(6)}(g)dV_g$
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- by Bin Guo and Haizhong Li PDF
- Proc. Amer. Math. Soc. 139 (2011), 2911-2925 Request permission
Abstract:
In this paper, we compute the second variational formula for the functional $\int _M v^{(6)}(g)dv_g$, which was introduced by Graham-Juhl; the first variational formula was obtained by Chang-Fang. We also prove that an Einstein manifold (with dimension $\ge 7$) is a strict local maximum within its conformal class unless the manifold is isometric to a round sphere with the standard metric up to a multiple of a constant.References
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Additional Information
- Bin Guo
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- Address at time of publication: Department of Mathematics, Rutgers University, 23995 BPO WAY, Piscataway, New Jersey 08854-8139
- Email: guob07@mails.tsinghua.edu.cn
- Haizhong Li
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- MR Author ID: 255846
- Email: hli@math.tsinghua.edu.cn
- Received by editor(s): July 14, 2010
- Published electronically: December 30, 2010
- Additional Notes: This work is supported by grant NSFC-10971110.
- Communicated by: Jianguo Cao
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2911-2925
- MSC (2010): Primary 53A30; Secondary 35J20, 35J60
- DOI: https://doi.org/10.1090/S0002-9939-2010-10703-7
- MathSciNet review: 2801632