Global existence and convergence for a higher order flow in conformal geometry
The main purpose of this paper is to construct conformal metrics for which the curvature quantity \(Q\) is a constant multiple of a prescribed positive function \(f\) on a compact n-dimensional manifold \(M\). In section 2 the author derives the evolution equation for the conformal factor and the curvature quantity \(Q\), next, in section 3 he shows that the solution is bounded in \(H^{n/2}\). In sections 4 and 5 the author shows that the solution exists for all time, and in section 6 he proves that the evolution equation converges to a stationary solution. Finally, in section 8 he proves a compactness theorem for conformal metrics on \(S^n\) (proposition 1.4).
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