Q-curvature Flow for GJMS Operators with Non-trivial Kernel

Abstract

We investigate the prescribed Q-curvature flow for GJMS operators with non-trivial kernel on compact manifolds of even dimension. When the total Q-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 and the convergence of the flow to a metric which is conformal to the initial one, and having a prescribed Q-curvature. If the total Q-curvature is positive, we show that the flow blows up in finite time.