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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
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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
Email: markovic@caltech.edu

DOI: https://doi.org/10.1090/jams/881
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 \textsl{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