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Parabolic super mean value inequality

Author: Chiung-Jue Sung
Journal: Proc. Amer. Math. Soc. 130 (2002), 3401-3408
MSC (2000): Primary 58J35
Published electronically: April 22, 2002
MathSciNet review: 1913020
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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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Additional Information

Chiung-Jue Sung
Affiliation: Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan 62117

Received by editor(s): December 29, 2000
Received by editor(s) in revised form: June 15, 2001
Published electronically: April 22, 2002
Additional Notes: The author’s research was partially supported by NSC grant.
Communicated by: Bennett Chow
Article copyright: © Copyright 2002 American Mathematical Society

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