Harmonic maps from R^n to H^m with symmetry
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چکیده
It is known that there is no nonconstant bounded harmonic map from the Euclidean space R to the hyperbolic space H. This is a particular case of a result of S.-Y. Cheng. However, there are many polynomial growth harmonic maps from R to H by the results of Z. Han, L.-F. Tam, A. Treibergs and T. Wan. One of the purposes of this paper is to construct harmonic maps from R to H by prescribing boundary data at infinity. The boundary data is assumed to satisfy some symmetric properties. On the other hand, it was proved by Han-Tam-Treibergs-Wan that under some reasonable assumptions, the image of a harmonic diffeomorphism from R into
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تاریخ انتشار 2001