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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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A steady length function for Ricci flows
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by Joshua Jordan PDF
Proc. Amer. Math. Soc. 149 (2021), 397-406 Request permission


A fundamental step in the analysis of singularities of Ricci flow was the discovery by Perelman of a monotonic volume quantity which detected shrinking solitons. A similar quantity was found by Feldman, Ilmanen, and Ni [J. Geom. Anal. 15 (2005), pp. 49–62] which detected expanding solitons. The current work introduces a modified length functional as a first step towards a steady soliton monotonicity formula. This length functional generates a distance function in the usual way which is shown to satisfy several differential inequalities which saturate precisely on manifolds satisfying a modification of the steady soliton equation.
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Additional Information
  • Joshua Jordan
  • Affiliation: Department of Mathematics, University of California Irvine, Irvine, California 92697-3875
  • ORCID: 0000-0001-6968-4672
  • Email:
  • Received by editor(s): April 4, 2020
  • Received by editor(s) in revised form: May 25, 2020
  • Published electronically: October 16, 2020
  • Communicated by: Jia-Ping Wang
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 397-406
  • MSC (2020): Primary 53E20
  • DOI:
  • MathSciNet review: 4172614