The prescribed Q-curvature flow for arbitrary even dimension in a critical case.

In this paper, we study the prescribed Q -curvature flow equation on a arbitrary even dimensional closed Riemannian manifold (M , g) , which was introduced by S. Brendle in [3] , where he proved the flow exists for long time and converges at infinity if the GJMS operator is weakly positive with trivial kernel and ∫ M Q d μ < (n − 1) ! Vol (S n). In this paper we study the critical case that ∫ M Q d μ = (n − 1) ! Vol (S n) , we will prove the convergence of the flow under some geometric hypothesis. In particular, this gives a new proof of Li-Li-Liu's existence result in [21] in dimension 4 and extend the work of Li-Zhu [22] in dimension 2 to general even dimensions. In the proof, we give a explicit expression of the limit of the corresponding energy functional when the blow up occurs. [ABSTRACT FROM AUTHOR]