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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Harmonic maps and the Schoen conjecture
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by Vladimir Markovic PDF
J. Amer. Math. Soc. 30 (2017), 799-817 Request permission

Abstract:

We show that every quasisymmetric homeomorphism of the circle $\partial {\mathbb {H}^2}$ admits a harmonic quasiconformal extension to the hyperbolic plane $\mathbb {H}^2$. This proves the Schoen conjecture.
References
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Additional Information
  • Vladimir Markovic
  • Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
  • MR Author ID: 620832
  • Email: markovic@caltech.edu
  • Received by editor(s): March 11, 2015
  • Received by editor(s) in revised form: July 22, 2016
  • Published electronically: March 1, 2017
  • Additional Notes: The author was partially supported by the Simons Investigator Award 409745 from the Simons Foundation, by the “Fund for Basic Research” from the Institute for Advanced Study, and by the NSF grant number DMS-1201463.
  • © Copyright 2017 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 30 (2017), 799-817
  • MSC (2010): Primary 53C43
  • DOI: https://doi.org/10.1090/jams/881
  • MathSciNet review: 3630088