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Liouville theorems for the ancient solution of heat flows


Author: Meng Wang
Journal: Proc. Amer. Math. Soc. 139 (2011), 3491-3496
MSC (2010): Primary 35K05, 58J35
DOI: https://doi.org/10.1090/S0002-9939-2011-11170-5
Published electronically: May 24, 2011
MathSciNet review: 2813381
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a complete Riemannian manifold with Ricci curvature bounded from below: $ Ric(M)\ge-\kappa$. Let $ N$ be a simply connected complete Riemannian manifold with nonpositive sectional curvature. Using a gradient estimate, we prove Liouville's theorem for the ancient solution of heat flows.


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Additional Information

Meng Wang
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Email: mathdreamcn@zju.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2011-11170-5
Keywords: Liouville theorem, ancient solution, quasi-harmonic map, heat flow
Received by editor(s): August 18, 2010
Published electronically: May 24, 2011
Additional Notes: The author’s research was partially supported by NSFC 10701064, 10931001
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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