Abstract
We prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.
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@ARTICLE{TamWan95, mrkey = {1366549},
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issn = {0022-040X},
author = {Tam, Luen-Fai and Wan, Tom Y. H.},
mrclass = {32G15 (30C65 30F60)},
url = {http://projecteuclid.org/euclid.jdg/1214457235},
journal = {J. Differential Geom.},
zblnumber = {0873.32019},
volume = {42},
mrnumber = {1366549},
fjournal = {Journal of Differential Geometry},
mrreviewer = {William P. Minicozzi, II},
coden = {JDGEAS},
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year = {1995},
pages = {368--410},
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@ARTICLE{Tukia85, mrkey = {0781586},
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mrclass = {30C60 (30F35)},
doi = {10.1007/BF02392471},
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zblnumber = {0562.30018},
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@ARTICLE{Wan92, mrkey = {1163452},
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mrclass = {58E20 (32G15 53A10)},
url = {http://projecteuclid.org/euclid.jdg/1214448260},
journal = {J. Differential Geom.},
zblnumber = {0808.53056},
volume = {35},
mrnumber = {1163452},
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coden = {JDGEAS},
title = {Constant mean curvature surface, harmonic maps, and universal {T}eichmüller space},
year = {1992},
pages = {643--657},
}