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
DOI:
https://doi.org/10.1090/S0002-9939-2011-11057-8
Published electronically:
June 9, 2011
MathSciNet review:
2846338
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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.
