Parabolic super mean value inequality
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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.References
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Additional Information
- Chiung-Jue Sung
- Affiliation: Department of Mathematics, National Chung Cheng University, Chia-Yi, Taiwan 62117
- MR Author ID: 357591
- Email: cjsung@math.ccu.edu.tw
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3401-3408
- MSC (2000): Primary 58J35
- DOI: https://doi.org/10.1090/S0002-9939-02-06457-2
- MathSciNet review: 1913020