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arXiv · 1305.0616

$L^p$-Liouville theorems on complete smooth metric measure spaces

Jia-Yong Wu
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Abstract

We study some function-theoretic properties on a complete smooth metric measure space $(M,g,e^{-f}dv)$ with Bakry-Émery Ricci curvature bounded from below. We derive a Moser's parabolic Harnack inequality for the $f$-heat equation, which leads to upper and lower Gaussian bounds on the $f$-heat kernel. We also prove $L^p$-Liouville theorems in terms of the lower bound of Bakry-Émery Ricci curvature and the bound of function $f$, which generalize the classical Ricci curvature case and the $N$-Bakry-Émery Ricci curvature case.

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Jia-Yong Wu. 2013-07-31. $L^p$-Liouville theorems on complete smooth metric measure spaces. https://doi.org/10.1016/j.bulsci.2013.07.002

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