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Published July 2017 | Submitted
Journal Article Open

Harmonic maps and the Schoen conjecture

Abstract

We show that every quasisymmetric homeomorphism of the circle ∂H^2 admits a harmonic quasiconformal extension to the hyperbolic plane H^2. This proves the Schoen conjecture.

Additional Information

© 2017 American Mathematical Society. Received by the editors March 11, 2015 and, in revised form, July 22, 2016. Published electronically: March 1, 2017. 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.

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Created:
August 19, 2023
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October 25, 2023