Admissible metrics in the $\sigma _{k}$-Yamabe equation
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Abstract:
In most previous works on the existence of solutions to the $\sigma _{k}$-Yamabe problem, one assumes that the initial metric $g_{0}$ is $k$-admissible. This is a pointwise condition. In this paper we prove that this condition can be replaced by a weaker integral condition.References
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Additional Information
- Weimin Sheng
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Email: weimins@zju.edu.cn
- Received by editor(s): January 30, 2007
- Received by editor(s) in revised form: February 21, 2007
- Published electronically: December 18, 2007
- Additional Notes: The author was supported in part by NSFC Grant #10471122.
- Communicated by: Richard A. Wentworth
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1795-1802
- MSC (2000): Primary 53C21; Secondary 53C20, 35J60
- DOI: https://doi.org/10.1090/S0002-9939-07-09167-8
- MathSciNet review: 2373610