微分几何观点下二元函数的极值

Differential Geometry and Extreme Values of Functions of Two Variables

利用曲面的局部微分性质给出二元函数极值存在的必要条件和充分条件,并将之运用于具有明显几何特征的曲面对应的二元函数极值的判别问题中.

Using the local properties of surface differentials, both sufficient and necessary conditions for the existence of extreme values of the corresponding functions of two variables are given. We apply our results to justify the existence of extreme values for functions with the corresponding surfaces having clear geometric significances.