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

 

Bounds on the heat kernel under the Ricci flow


Author: Mihai Băileşteanu
Journal: Proc. Amer. Math. Soc. 140 (2012), 691-700
MSC (2010): Primary 53C44, 35K05, 35K08; Secondary 53B20, 53B21
Published electronically: June 9, 2011
MathSciNet review: 2846338
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Abstract: We establish an estimate for the fundamental solution of the heat equation on a closed Riemannian manifold $ M$ of dimension at least $ 3$, evolving under the Ricci flow. The estimate depends on some constants arising from a Sobolev imbedding theorem. Considering the case when the scalar curvature is positive throughout the manifold, at any time, we will obtain, as a corollary, a bound similar to the one known for the fixed metric case.


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Additional Information

Mihai Băileşteanu
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email: mbailesteanu@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11057-8
PII: S 0002-9939(2011)11057-8
Received by editor(s): November 23, 2010
Published electronically: June 9, 2011
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.