Conformal Bach flow

Jiaqi Chen; Peng Lu; Jie Qing

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arXiv · 2104.08968

Conformal Bach flow

Jiaqi Chen·Peng Lu·Jie Qing

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Abstract

In this article 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 behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi's type $L^2$-estimate of derivatives of curvatures are derived. Furthermore using the $L^2$-estimate and based on an idea from \cite{St13} we show Shi's pointwise-estimate of derivatives of curvatures without assuming Sobolev constant bound.

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Jiaqi Chen, Peng Lu, Jie Qing. 2021-04-18. Conformal Bach flow. https://arxiv.org/abs/2104.08968

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