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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Prescribing the symmetric function of the eigenvalues of the Schouten tensor


Authors: Yan He and Weimin Sheng
Journal: Proc. Amer. Math. Soc. 139 (2011), 1127-1136
MSC (2010): Primary 53C21; Secondary 35J60
Published electronically: October 27, 2010
MathSciNet review: 2745665
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Abstract: In this paper we study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Schouten tensor on compact Riemannian manifolds with boundary. We prove its solvability and the compactness of the solution set, provided the Ricci tensor is nonnegative-definite.


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Additional Information

Yan He
Affiliation: Centre for Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China
Email: helenaig@zju.edu.cn

Weimin Sheng
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
Email: weimins@zju.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10674-3
PII: S 0002-9939(2010)10674-3
Keywords: Conformal geometry, prescribing curvature, Ricci tensor
Received by editor(s): January 31, 2010
Published electronically: October 27, 2010
Additional Notes: This work was partially supported by NSFC Grants 10771189 and 10831008.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.