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Published March 2015 | public
Journal Article Open

Harmonic maps between 3-dimensional hyperbolic spaces

Abstract

We prove that a quasiconformal map of the sphere S^2 admits a harmonic quasi-isometric extension to the hyperbolic space H^3, thus confirming the well known Schoen Conjecture in dimension 3.

Additional Information

© 2014 Springer-Verlag Berlin Heidelberg. Received: 7 August 2013; Accepted: 29 June 2014; Published online: 15 July 2014. Vladimir Markovic is supported by the NSF grant number DMS-1201463. I am grateful to the referee for his/her comments and suggestions. Most of this project was carried out while the author was visiting University of Minnesota in Minneapolis as the Ordway Visiting Professor. I wish to thank them for their hospitality.

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