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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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Soliton solutions to the curve shortening flow on the sphere
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by Hiuri Fellipe Santos dos Reis and Keti Tenenblat PDF
Proc. Amer. Math. Soc. 147 (2019), 4955-4967 Request permission

Abstract:

It is shown that a curve on the unit sphere is a soliton solution to the curve shortening flow if and only if its geodesic curvature is proportional to the inner product between its tangent vector and a fixed vector of $\mathbb {R}^3$. Using this characterization, we describe the geometry of such a curve on the sphere, we study its qualitative behavior, and we prove the convergence of the curve to the equator orthogonal to the fixed vector.
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Additional Information
  • Hiuri Fellipe Santos dos Reis
  • Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
  • MR Author ID: 1287830
  • Email: hiuri.reis@ifg.edu.br
  • Keti Tenenblat
  • Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
  • MR Author ID: 171535
  • Email: K.Tenenblat@mat.unb.br
  • Received by editor(s): December 10, 2018
  • Received by editor(s) in revised form: February 9, 2019, and February 22, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: The first author was partially supported by CNPq Proc. 141275/2014-6, Ministry of Science and Technology, Brazil
    The second author was partially supported by CNPq Proc. 312462/2014-0, Ministry of Science and Technology, Brazil and FAPDF/Brazil grant 0193.001346/2016.
  • Communicated by: Jiaping Wang
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4955-4967
  • MSC (2010): Primary 53C44
  • DOI: https://doi.org/10.1090/proc/14607
  • MathSciNet review: 4011527