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Parabolic Frequency Monotonicity on Ricci Flow and Ricci-Harmonic Flow with Bounded Curvatures

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Abstract

In this paper, we study the monotonicity of parabolic frequency motivated by Baldauf and Kim (Parabolic frequency on Ricci flows. To appear in Int. Math. Res. Not., rnac128. https://doi.org/10.1093/imrn/rnac128) under the Ricci flow and the Ricci-harmonic flow on manifolds. Here we consider two cases: one is the monotonicity of parabolic frequency for the solution of linear heat equation with bounded Bakry-Émery Ricci curvature, and another case is the monotonicity of parabolic frequency for the solution of heat equation with bounded Ricci curvature.

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Acknowledgements

The second author is supported in part by National Science Foundation of China (NSFC Grant No. 92066106 and No. 12271093).

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Chuanhuan Li

  2. School of Mathematics and Shing-Tung Yau Center of Southeast University, Southeast University, Nanjing, 211189, China

    Yi Li

  3. School of Mathematics, Southeast University, Nanjing, 211189, China

    Kairui Xu

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  1. Chuanhuan Li
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  2. Yi Li
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  3. Kairui Xu
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Correspondence to Yi Li.

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Li, C., Li, Y. & Xu, K. Parabolic Frequency Monotonicity on Ricci Flow and Ricci-Harmonic Flow with Bounded Curvatures. J Geom Anal 33, 282 (2023). https://doi.org/10.1007/s12220-023-01345-3

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