摘要
This paper studies the uniqueness of the harmonic maps from R<sup>n</sup> into S<sup>n-1</sup>. At first it is proved that the map ψ（x）=x|x|:B<sup>n</sup>→S<sup>n-1</sup> is the unique energy minimizing harmonic map. Then the uniqueness of the harmonic maps with identity boundary value from B<sup>n</sup> to S<sup>n-1</sup> follows.
This paper studies the uniqueness of the harmonic maps from R(n) into S(n-1). At first it is proved that the map psi-(x) = \x\/x: B(n) --> S(n-1) is the unique energy minimizing harmonic map. Then the uniqueness of the harmonic maps with identity boundary value from B(n) to S(n-1) follows.
基金
Supported by the National Natural Science Foundation of China
