We introduce conformal Bach flow and establish its well-posedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behaviour of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type L2-estimate of derivatives of curvatures are derived. To make the talk more accessible, we will spend some time to survey on high-order parabolic curvature flow.
This is a joint work with Jiaqi Chen of Xiamen University and Jie Qing of UCSC. This talk is based on this arXiv paper.
This video was produced by the Sydney Mathematical Research Institute, as part of their SMRI seminar series.
