Conformal Bach flow

Abstract. In this article we introduce conformal Bach flow and establish its wellposedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type L-estimate of derivatives of curvatures are derived. Furthermore using the L-estimate and based on an idea from [St13] we show Shi’s pointwise-estimate of derivatives of curvatures without assuming Sobolev constant bound.

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