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Parabolic super mean value inequality
Author(s):
Chiung-Jue
Sung
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3401-3408.
MSC (2000):
Primary 58J35
Posted:
April 22, 2002
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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
Email:
cjsung@math.ccu.edu.tw
DOI:
10.1090/S0002-9939-02-06457-2
PII:
S 0002-9939(02)06457-2
Received by editor(s):
December 29, 2000
Received by editor(s) in revised form:
June 15, 2001
Posted:
April 22, 2002
Additional Notes:
The author's research was partially supported by NSC grant.
Communicated by:
Bennett Chow
Copyright of article:
Copyright
2002,
American Mathematical Society
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