The fourth-order $Q$-curvature flow on closed 3-manifolds

Abstract

Let the Paneitz operator $P_{0}$ be strictly positive on a closed 3-manifold $M$ with a fixed conformal class. It is proved that the solution of a fourth-order $Q$-curvature flow exists on $M$ for all time and converges smoothly to a metric of constant $Q$-curvature.