QQ-curvature flow for GJMS operators with non-trivial kernel

We investigate the prescribed QQ-curvature flow for GJMS operators with non-trivial kernel on a compact manifold of even dimension. When the total QQ-curvature is negative, we identify a conformally invariant condition on the nodal domains of functions in the kernel of the GJMS operator, allowing us to prove the global existence of the flow and its convergence at infinity to a metric which is conformal to the initial one, and having a prescribed QQ-curvature. If the total QQ-curvature is positive, we show that the flow blows up in finite time.