中文摘要：

设x：M—A n＋1是一个局部严格凸超曲面，由Ω An上的凸函数Xn＋1=f（x1，x2，…，xn）定义．作者研究了由△ρ=λ｜｜ρ｜｜ G2 /ρ所定义的相对极值超曲面解的问题，这里入是常值，△是局部严格凸超曲面上的关于Blaschke度量G的Laplacian算子．

英文摘要：

Let x.M--A n＋1 be a locally strongly convex hypersrface, given by a convex function xn＋1 =f（x1 ,x2 ,… ,xn） defined in a convex domain Ω An. The purpose of this paper is to study the solution of the relative extremal hypersurface equation given by △ρ=λ｜｜ρ｜｜ G2 /ρ ,where X is a constant and A denotes the Laplaian operator with respect to the Blaschke metric G of the locally strongly convex hypersurface