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Hopf differentials and the images of harmonic maps. (English) Zbl 1040.58004
The authors prove a variety of results on the image of harmonic maps of into H 2 assuming that the Hopf differential has faster than polynomial growth. Under various growth conditions, non-surjectivity of the harmonic map is derived. As a byproduct of the study of the Hopf differentials, various results are derived on quasi-conformal harmonic diffeomorphisms of H 2 .
MSC:
58E20Harmonic maps between infinite-dimensional spaces
30F30Differentials on Riemann surfaces