## Davies type estimate and the heat kernel bound under the Ricci flow

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## Abstract:

We prove a Davies type double integral estimate for the heat kernel $H(y,t;x,l)$ under the Ricci flow. As a result, we give an affirmative answer to a question proposed by Chow et al. Moreover, we apply the Davies type estimate to provide a new proof of the Gaussian upper and lower bounds of $H(y,t;x,l)$ which were first shown in 2011 by Chan, Tam, and Yu.## References

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## Additional Information

**Meng Zhu**- Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China – and – Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
- Address at time of publication: Department of Mathematics, University of California, Riverside, California 92521
- MR Author ID: 888985
- Email: mzhu@math.ecnu.edu.cn, mengzhu@ucr.edu
- Received by editor(s): December 30, 2013
- Published electronically: May 20, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 1663-1680 - MSC (2010): Primary 53C44, 58J35
- DOI: https://doi.org/10.1090/tran/6600
- MathSciNet review: 3449222