F-完备抛物仿射超球的Bernstein性质（英文）

Bernstien properties of F-complete parabolic affine hyperspheres

设x:M→R^(n+1)是局部强凸超曲面,由定义在凸域DR^n上的局部强凸函数x^(n+1)=f(x_1,x_2,…,x_n)给出.本文在M上定义F-度量G=F(ρ)∑i,j,~2 f/x_ix_jdx_idx_j,研究F-完备抛物仿射超球并得到了相应的Bernstein性质.

Let x. M→Rn＋1 be a locally strongly convex hypersurface given by the graph of a locallystrongly convex function Xn＋1 =f（x1 ,χ2, ……,xn） defined in a convex domain DCRn. Defining the F-metric dxidxj on M, we derive the PDEs of the F-complete parabolic affine hypersph eres and obtain some Bernstein properties.