301. A Fourth Order Curvature Flow on a CR 3-manifold
- Author
-
Chang, Shu-Cheng, Cheng, Jih-Hsin, and Chiu, Hung-Lin
- Subjects
Mathematics - Differential Geometry ,Mathematics - Complex Variables ,32V20 ,53C44 - 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 up to high orders for the solution., Comment: 35 pages
- Published
- 2005