IUMJ

Title: A fourth order curvature flow on a CR 3-manifold

Authors: Shu-Cheng Chang, Jih-Hsin Cheng and Hung-Lin Chiu

Issue: Volume 56 (2007), Issue 4, 1793-1826

Abstract:

Let $(\mathbf{M}^3, J, \theta_0)$ be a closed pseudohermitian $3$-manifold. Suppose the associated torsion vanishes and the associated $Q$-curvature has no kernel part with respect to the associated Paneitz operator. On such a background pseudohermitian $3$-manifold, we study the change of the contact form according to a certain version of normalized $Q$-curvature flow. This is a fourth order evolution equation. We prove that the solution exists for all time and converges smoothly to a contact form of zero $Q$-curvature. We also consider other background conditions and obtain a priori bounds on high-order norms on the solutions.