%0 Journal Article
%T A Fourth Order Curvature Flow on a CR 3-manifold
%A Shu-Cheng Chang
%A Jih-Hsin Cheng
%A Hung-Lin Chiu
%J Mathematics
%D 2005
%I arXiv
%X 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 up to high orders for the solution.
%U http://arxiv.org/abs/math/0510494v1