ON A CLASS OF ROTATION ALLY SYMMETRIC p-HARMONIC MAPS

We give a classification of rotationally symmetric p-harmonic maps between some model spaces such as R-n and H-n by their asymptotic behaviors. Among others, we show that, when p > 2 and n >= 2, all rotationally symmetric p-harmonic maps from R-n to H-n have to blow up at a finite point, while all rotationally symmetric p-harmonic maps from H-n to H-n observe the trichotomy property, i.e. the map y is the identity map, is bounded or blows up according as its initial value y'(0) is equal to, less than or greater than one. Our sharp estimates imply and improve a number of existence and non-existence results of certain p-harmonic maps on noncompact manifolds.