A remark on the nonnegativity of the Paneitz operator

Lai, Mijia

doi:10.1090/S0002-9939-2015-12604-4

A remark on the nonnegativity of the Paneitz operator
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by Mijia Lai

Proc. Amer. Math. Soc. 143 (2015), 4893-4900

DOI: https://doi.org/10.1090/S0002-9939-2015-12604-4

Published electronically: April 1, 2015

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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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