Parabolic super mean value inequality

Sung, Chiung-Jue

doi:10.1090/S0002-9939-02-06457-2

Parabolic super mean value inequality
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Proc. Amer. Math. Soc. 130 (2002), 3401-3408 Request permission

Abstract:

In this note, we show that a type of mean value inequality for the positive supersolutions to the heat equation on a Riemannian manifold is equivalent to a version of local heat kernel lower bounds. We also show that the global Gaussian type heat kernel lower bound implies that the manifold has the Liouville property.

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