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Harmonic maps between 3-dimensional hyperbolic spaces

Markovic, Vladimir (2015) Harmonic maps between 3-dimensional hyperbolic spaces. Inventiones Mathematicae, 199 (3). pp. 921-951. ISSN 0020-9910. https://resolver.caltech.edu/CaltechAUTHORS:20150416-105100093

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00222-014-0536-x DOIArticle
http://link.springer.com/article/10.1007%2Fs00222-014-0536-xPublisherArticle
http://arxiv.org/abs/1308.1710arXivArticle
http://rdcu.be/rO4XPublisherFree ReadCube access
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1201463
Issue or Number:3
Classification Code:Mathematics Subject Classification (2000): Primary 53C43
Record Number:CaltechAUTHORS:20150416-105100093
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150416-105100093
Official Citation:Markovic, V. Invent. math. (2015) 199: 921. doi:10.1007/s00222-014-0536-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56723
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Apr 2015 17:55
Last Modified:03 Oct 2019 08:16

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