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A remark on the nonnegativity of the Paneitz operator


Author: Mijia Lai
Journal: Proc. Amer. Math. Soc. 143 (2015), 4893-4900
MSC (2010): Primary 53A30
DOI: https://doi.org/10.1090/S0002-9939-2015-12604-4
Published electronically: April 1, 2015
MathSciNet review: 3391047
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Abstract: In this short article, we interpret the condition of a theorem of Gursky-Viaclovsky concerning the nonnegativity of the Paneitz operator as the metric being $ 3$-positive Ricci. By a result of Wolfson, this condition can be preserved under the surgery of codimension $ q\geq 3$. Combining these two observations, we expand the list of manifolds which admit metrics with a nonnegative Paneitz operator. Consequently, there exist metrics of constant $ Q$-curvature on these manifolds.


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Additional Information

Mijia Lai
Affiliation: Department of Mathematics, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China
Email: laimijia@sjtu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2015-12604-4
Received by editor(s): April 24, 2014
Received by editor(s) in revised form: July 15, 2014, and July 31, 2014
Published electronically: April 1, 2015
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society

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