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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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Evolution of closed curves by length-constrained curve diffusion
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by James McCoy, Glen Wheeler and Yuhan Wu PDF
Proc. Amer. Math. Soc. 147 (2019), 3493-3506 Request permission

Abstract:

We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We provide an estimate on the total length of time for which such curves are not strictly convex. We further show that there are no closed translating solutions to the flow and that the only closed rotators are circles.
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Additional Information
  • James McCoy
  • Affiliation: School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, New South Wales, 2308 Australia
  • MR Author ID: 724395
  • Email: james.mccoy@newcastle.edu.au
  • Glen Wheeler
  • Affiliation: Institute for Mathematics and its Applications, University of Wollongong, Wollongong, New South Wales, 2522 Australia
  • MR Author ID: 833897
  • Email: glenw@uow.edu.au
  • Yuhan Wu
  • Affiliation: Institute for Mathematics and its Applications, University of Wollongong, Wollongong, New South Wales, 2522 Australia
  • MR Author ID: 1145911
  • Email: yw120@uowmail.edu.au
  • Received by editor(s): June 28, 2018
  • Received by editor(s) in revised form: November 11, 2018
  • Published electronically: March 15, 2019
  • Additional Notes: Some of this research was conducted while the first author was visiting the University of Wollongong. The first author is the corresponding author. The research of the first and second authors was supported by Discovery Project grant DP150100375 of the Australian Research Council.
    The research of the third author was supported by a University of Wollongong Faculty of Engineering and Information Sciences Postgraduate research scholarship.
  • Communicated by: Guofang Wei
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 3493-3506
  • MSC (2010): Primary 53C44, 58J35
  • DOI: https://doi.org/10.1090/proc/14473
  • MathSciNet review: 3981127