固定边界的曲面中面积最小曲面的必要条件

The Necessary Condition of Minimal Curved Surface Within the Curved Surface with Fixed Boundary

考虑固定边界的曲面中面积最小曲面的必要条件的证明方法问题.在三维欧氏空间中,给定边界的闭曲面中面积最小的曲面,其平均曲率一定为零.采用直接的曲面向量方程的扰动方法,给出了固定边界面积最小曲面的必要条件的证明过程.

The proof method of the necessary condition of minimal curved surface within the curved surface with fixed boundary is discussed in this paper. In three-dimensional Euclidean space, the mean curvature of minimal curved surface within the closed curved surface with fixed boundary is bound to be zero. The proof process of the necessary condition of minimal curved surface within the curved surface with fixed boundary is demonstrated by means of the direct perturbation method of the surface vector equation.