Abstract
We give a monotonicity entropy formula for the linear heat equation on complete manifolds with Ricci curvature bounded from below. As its applications, we get a differential Harnack inequality and a lower bound estimate about the heat kernel.
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This work was completed with the support of the NSF of China (10871070, 10971066).
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Wang, LF. A new entropy formula for the linear heat equation. Arch. Math. 96, 473–481 (2011). https://doi.org/10.1007/s00013-011-0263-0
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DOI: https://doi.org/10.1007/s00013-011-0263-0