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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Davies type estimate and the heat kernel bound under the Ricci flow
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by Meng Zhu PDF
Trans. Amer. Math. Soc. 368 (2016), 1663-1680 Request permission

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
  • 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