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 | References | Similar Articles | Additional Information

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

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.