中文摘要：

本文研究了欧氏空间R3中曲面的法向变分曲面的面积和体积的极值问题，利用变分的方法，得到了正则曲面为极小曲面的一个充分必要条件，以及正则曲面取得极小面积的几个充分条件．

英文摘要：

In this paper, we investigate the extremum problem of area and enclosed volume of the normal variation of a surface in the Euclidean space R3. We obtain a sufficient and necessary condition for a surface to be a minimal surface. We also obtain some sufficient conditions when the surface area attains extremum.