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
Published electronically:
May 24, 2011
MathSciNet review:
2813381
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let 
be a complete Riemannian manifold with Ricci curvature bounded from below: 
. Let 
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:
http://dx.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.