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MR1063050 (91g:58062) 58E20 (58G32 60G48 60J45)
Kendall, Wilfrid S. Probability, convexity, and harmonic maps with small image. I. Uniqueness and fine existence. Proc. London Math. Soc. (3) 61 (1990), no. 2, 371--406.
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