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