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An upper bound of the heat kernel along the harmonic-Ricci flow

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Abstract

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser’s iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

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Author information

Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, People’s Republic of China

    Shouwen Fang

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Tao Zheng

Authors
  1. Shouwen Fang
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  2. Tao Zheng
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Corresponding author

Correspondence to Tao Zheng.

Additional information

Shouwen Fang: The work is supported by NSFC Grant No. 11401514.

Tao Zheng: The work is supported by NSFC Grant No. 11401023 and China Postdoctoral Science Foundation funded Project No. 2015T80040.

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Fang, S., Zheng, T. An upper bound of the heat kernel along the harmonic-Ricci flow. manuscripta math. 151, 1–18 (2016). https://doi.org/10.1007/s00229-016-0825-3

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  • DOI: https://doi.org/10.1007/s00229-016-0825-3

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