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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bounds on the heat kernel under the Ricci flow
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by Mihai Băileşteanu PDF
Proc. Amer. Math. Soc. 140 (2012), 691-700 Request permission


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:
  • Received by editor(s): November 23, 2010
  • Published electronically: June 9, 2011
  • Communicated by: Chuu-Lian Terng
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 691-700
  • MSC (2010): Primary 53C44, 35K05, 35K08; Secondary 53B20, 53B21
  • DOI:
  • MathSciNet review: 2846338