一类偏微分方程的解的Bernstein性质  

Bernstein Property for Solutions of a Partial Differential Equation

作　　者：胡传峰[1] 姬秀[1] 

机构地区：[1]长江大学文理学院,湖北荆州434000

出　　处：《中北大学学报（自然科学版）》2016年第3期220-224,共5页Journal of North University of China(Natural Science Edition)

基　　金：湖北省教育厅科学技术研究基金资助项目(B2016458)

摘　　要：在局部严格凸的超曲面M上定义了α-相对度量G~α.研究了关于G~α完备且α-Ricci曲率有下界-N的超曲面M.利用活动标架法及J-C-P定理,证明了当ρ满足一个四阶偏微分方程时,M一定是椭圆抛物面.A a-relative metric Ga was defined on a locally strongly convex hypersurface M. Let M be com- plete with respect to Ga and its a-Ricci curvature was hounded from below by a constant-N. By moving frames and J-C-P theorem, it drawed that the conclusion that M must be an elliptic paraboloid, when p satisfied a fourth order partial differential equation.

关 键 词：Bernstein性质 相对极值超曲面 偏微分方程 EULER-LAGRANGE方程 

分 类 号：O186.13[理学—数学]