Sharp Hamilton’s Laplacian estimate for the heat kernel on complete manifolds
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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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 4401-4409
- MSC (2010): Primary 58J35; Secondary 35K08
- DOI: https://doi.org/10.1090/S0002-9939-2013-11926-X
- MathSciNet review: 3105882