给定边界面积最小的曲面的平均曲率为零的证明方法  

New Ways to Prove the Mean Curvature (H≡0) of the Minimal Surfaces Under Prescribed Boundary Condition

作　　者：邢家省[1,2] 贺慧霞[1,2] 高建全[3] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191 [2]数学,信息与行为教育部重点实验室,北京100191 [3]平顶山教育学院,河南平顶山467000

出　　处：《四川理工学院学报（自然科学版）》2014年第2期83-86,90,共5页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11171013)

摘　　要：在曲面论几何中,定义平均曲率为零的曲面为极小曲面。而在三维欧氏空间中,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,即给定边界的闭曲面中面积最小的曲面为极小曲面。文章用变分理论给出几种新的证明,使证明过程更加直接明了。In surface theory, the minimal surfaces are the surfaces with mean curvatures H = O. It＇s also well known that mean curvatures of the closed surfaces with minimal area under prescribed boundary must be zero, it means that the closed surfaces with minimal area under prescribed boundary are minimal ods to prove this conclusion are given. These new ways make the surfaces. By using the variation theory, several new meth- process of proof more directly and clear.

关 键 词：极小曲面 正则曲面 平均曲率 变分方法 

分 类 号：O186.1[理学—数学]