摘要
该文考虑如下预定曲率方程S_k(λ{h_(ij)})(X)=f(X),X∈M R^(n+1),应用Hamilton张量极大值原理证明了带边界情形下,如果M的第二基本形式h_(ij)半正定,则有解曲面M凸.从而,不难得到常平均曲率方程的解曲面凸.
In this article, the author investigates the solution surface of the prescribed curvature equation Sk （λ{hij}）（X）=f（X）,VX∈M包含Rn＋1 It is proved that the solution surfaceM of the prescribed curvature equation in Rn＋l is convex under the condition that the second fundamental form hij of M is semi-positive definite on the boundary OM. The author makes use of Hamilton tensor maximum principle to prove this result. As a consequence, the convexity for the solution surface of constant mean curvature in Rn＋l is easily obtained. Key words： Convexity; Curvature equation; Maximum principle
出处
《数学物理学报（A辑）》
CSCD
北大核心
2011年第5期1176-1180,共5页
Acta Mathematica Scientia
基金
国家自然科学基金(10671186)资助
关键词
凸性
曲率方程
极大值原理.
Convexity
Curvature equation
Maximum principle
