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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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