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Harmonic maps into hyperbolic 3-manifolds. (English) Zbl 0762.53040
Fix a nondegenerate homotopy class $$H$$ of maps of a closed surface $$S$$ into a complete hyperbolic 3-manifold $$N$$. Then for each conformal structure $$\sigma$$ on $$S$$ there is a unique harmonic map in $$H$$. This paper examines the behaviour of these as $$\sigma$$ goes to infinity in the Teichmüller space of $$S$$. The author obtains results relating the shape of images of high-energy harmonic maps to those of pleated surfaces. The main results are based on and are direct generalizations of those of the author [J. Differ. Geom. 35, 151-217 (1992)] which should serve as an introduction and a prerequisite. This is a fine contribution, and well written.

##### MSC:
 53C40 Global submanifolds 58E20 Harmonic maps, etc. 30F60 Teichmüller theory for Riemann surfaces
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