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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sharp Hamilton's Laplacian estimate for the heat kernel on complete manifolds


Author: Jia-Yong Wu
Journal: Proc. Amer. Math. Soc. 141 (2013), 4401-4409
MSC (2010): Primary 58J35; Secondary 35K08
Published electronically: August 20, 2013
MathSciNet review: 3105882
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Abstract: In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative Ricci curvature that is sharp in the order of time parameter for the heat kernel on the Euclidean space.


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Additional Information

Jia-Yong Wu
Affiliation: Department of Mathematics, Shanghai Maritime University, Haigang Avenue 1550, Shanghai 201306, People’s Republic of China
Email: jywu81@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11926-X
PII: S 0002-9939(2013)11926-X
Keywords: Gradient estimate, heat kernel, heat equation
Received by editor(s): February 10, 2012
Published electronically: August 20, 2013
Additional Notes: This work was partially supported by the NSFC (11101267, 11271132) and the Innovation Program of Shanghai Municipal Education Commission (13YZ087)
Communicated by: Lei Ni
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.