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Conformal Bach flow

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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 is derived. Furthermore, using the \(L^2\)-estimate and based on an idea from (Streets in Calc Var PDE 46:39–54, 2013) we show Shi’s pointwise estimate of derivatives of curvatures without assuming Sobolev constant bound.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Xiamen University of Technology, Xiamen, 361024, Fujian, China

    Jiaqi Chen

  2. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Peng Lu

  3. Department of Mathematics, University of California, Santa Cruz, CA, 95064, USA

    Jie Qing

Authors
  1. Jiaqi Chen
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  2. Peng Lu
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  3. Jie Qing
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Correspondence to Peng Lu.

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P.L. is partially supported by Simons Foundation through Collaboration Grant 229727. J.Q. is partially supported by NSF DMS-1608782.

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Chen, J., Lu, P. & Qing, J. Conformal Bach flow. Ann Glob Anal Geom 63, 19 (2023). https://doi.org/10.1007/s10455-023-09897-x

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  • DOI: https://doi.org/10.1007/s10455-023-09897-x

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