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Journal of the American Mathematical Society

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Harmonic maps and the Schoen conjecture


Author: Vladimir Markovic
Journal: J. Amer. Math. Soc. 30 (2017), 799-817
MSC (2010): Primary 53C43
DOI: https://doi.org/10.1090/jams/881
Published electronically: March 1, 2017
MathSciNet review: 3630088
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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.


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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.
Article copyright: © Copyright 2017 American Mathematical Society