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Admissible metrics in the $ \sigma_{k}$-Yamabe equation


Author: Weimin Sheng
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
Published electronically: December 18, 2007
MathSciNet review: 2373610
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-07-09167-8
Keywords: $\sigma_{k}$-curvature, admissible metrics, $k$-Yamabe constant
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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