# Remarks on GJMS operator of order six

@article{Chen2016RemarksOG, title={Remarks on GJMS operator of order six}, author={Xuezhang Chen and Fei Hou}, journal={arXiv: Differential Geometry}, year={2016} }

We study analysis aspects of the sixth order GJMS operator $P_g^6$. Under conformal normal coordinates around a point, the expansions of Green's function of $P_g^6$ with pole at this point are presented. As a starting point of the study of $P_g^6$, we manage to give some existence results of prescribed $Q$-curvature problem on Einstein manifolds. One among them is that for $n \geq 10$, let $(M^n,g)$ be a closed Einstein manifold of positive scalar curvature and $f$ a smooth positive function in… Expand

#### One Citation

Existence result for the higher-order $Q$-curvature equation

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We obtain an existence result for the $Q$-curvature equation of arbitrary order $2k$ on a closed Riemannian manifold of dimension $n\ge 2k+4$, where $k\ge1$ is an integer. We obtain this result under… Expand

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