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Transactions of the American Mathematical Society

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


Author: Meng Zhu
Journal: Trans. Amer. Math. Soc. 368 (2016), 1663-1680
MSC (2010): Primary 53C44, 58J35
DOI: https://doi.org/10.1090/tran/6600
Published electronically: May 20, 2015
MathSciNet review: 3449222
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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.


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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
Email: mzhu@math.ecnu.edu.cn, mengzhu@ucr.edu

DOI: https://doi.org/10.1090/tran/6600
Keywords: Ricci flow, heat kernel, Davies type estimate, Gaussian bound
Received by editor(s): December 30, 2013
Published electronically: May 20, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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