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

Zhu, Meng

doi:10.1090/tran/6600

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