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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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First eigenvalues of geometric operators under the Ricci flow
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by Xiaodong Cao PDF
Proc. Amer. Math. Soc. 136 (2008), 4075-4078 Request permission

Abstract:

In this paper, we prove that the first eigenvalues of $-\Delta + cR$ ($c\geq \frac 14$) are nondecreasing under the Ricci flow. We also prove the monotonicity under the normalized Ricci flow for the cases $c= 1/4$ and $r\le 0$.
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Additional Information
  • Xiaodong Cao
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
  • MR Author ID: 775164
  • Email: cao@math.cornell.edu
  • Received by editor(s): October 5, 2007
  • Published electronically: June 2, 2008
  • Additional Notes: This research was partially supported by an MSRI postdoctoral fellowship
  • Communicated by: Chuu-Lian Terng
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 4075-4078
  • MSC (2000): Primary 58C40; Secondary 53C44
  • DOI: https://doi.org/10.1090/S0002-9939-08-09533-6
  • MathSciNet review: 2425749