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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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Nondegeneracy of half-harmonic maps from $\mathbb {R}$ into $\mathbb {S}^1$
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by Yannick Sire, Juncheng Wei and Youquan Zheng PDF
Proc. Amer. Math. Soc. 146 (2018), 5263-5268 Request permission

Abstract:

We prove that the standard half-harmonic map $U:\mathbb {R}\to \mathbb {S}^1$ defined by \begin{equation*} x\to \begin {pmatrix} \frac {x^2-1}{x^2+1} \\[4pt] \frac {-2x}{x^2+1} \end{pmatrix} \end{equation*} is nondegenerate in the sense that all bounded solutions of the linearized half-harmonic map equation are linear combinations of three functions corresponding to rigid motions (dilation, translation, and rotation) of $U$.
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Additional Information
  • Yannick Sire
  • Affiliation: Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, Baltimore, Maryland 21218
  • MR Author ID: 734674
  • Email: sire@math.jhu.edu
  • Juncheng Wei
  • Affiliation: Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada
  • MR Author ID: 339847
  • ORCID: 0000-0001-5262-477X
  • Email: jcwei@math.ubc.ca
  • Youquan Zheng
  • Affiliation: School of Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
  • Email: zhengyq@tju.edu.cn
  • Received by editor(s): December 20, 2017
  • Received by editor(s) in revised form: April 5, 2018
  • Published electronically: September 17, 2018
  • Additional Notes: The third author was partially supported by NSF of China (11301374) and China Scholarship Council (CSC)
  • Communicated by: Joachim Krieger
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 5263-5268
  • MSC (2010): Primary 35B06
  • DOI: https://doi.org/10.1090/proc/14184
  • MathSciNet review: 3866865