通过以上方程，仍然难由上面公式，显见如果 使得 取极小，则 满足式（5

通过以上方程，仍然难由上面公式，显见如果 使得 取极小，则 满足式（5）；同样容易证明，如果 使得 取极小，则 满足式（6）；因而，如果 使得 和 取最小值，则功是调和的。以求得调和映射的具体表达形式。为了得到调和映射的解析形式，对其进行处理得到：

結果 (英文) 1:

Through the above equation will still be from the above formula, it is evident that if you take minimum, satisfy (5) as easy to prove that if you take minimum, satisfy (6); thus, if made and take the minimum value, then the work is a blend of. In order to achieve specific expression of harmonic maps. In order to get the analytic form of harmonic maps, to get it:

結果 (英文) 2:

By the above equation, the above equation is still difficult, if such has a minimum apparent, then satisfies the formula (5); equally easy to show that if such has a minimum, satisfy the formula (6); Thus, if such a minimum value, and, the function is to reconcile. Harmonic maps in order to achieve the specific form of expression. In order to obtain the analytical form of harmonic maps, it is processed to obtain:

結果 (英文) 3:

Through the above equation, is still difficult to by the above formula, obvious if the minimum, then satisfy (5); also easy to prove that, if the minimum, then satisfy (6); therefore, if making and minimum value is harmonic, power. In order to obtain the harmonic mapping specific forms of expression. In order to obtain the analytical form of harmonic maps, carries on the treatment to obtain: