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Harmonic maps between 3-dimensional hyperbolic spaces

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

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, Pasadena, CA, 91125, USA

    Vladimir Markovic

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  1. Vladimir Markovic
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Correspondence to Vladimir Markovic.

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Vladimir Markovic is supported by the NSF grant number DMS-1201463.

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Markovic, V. Harmonic maps between 3-dimensional hyperbolic spaces. Invent. math. 199, 921–951 (2015). https://doi.org/10.1007/s00222-014-0536-x

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  • DOI: https://doi.org/10.1007/s00222-014-0536-x

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