F-相对极值超曲面的Bernstein性质(英文)  

Bernstein Property for F-relative Extremal Hypersurfaces

作　　者：胡传峰[1] 姬秀[1] 

机构地区：[1]长江大学文理学院,荆州湖北434000

出　　处：《数学进展》2016年第1期143-152,共10页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11171207);Project of Hubei Provincial Department of Education(No.B2014281)

摘　　要：设x:M→R^(n+1)是一个局部严格凸的超曲面,由定义在一个凸域Ω()R^n上的严格凸函数x_(n+1)=f(x_1,x_2,…,x_n)给出.设Y=(0,0,…,0,1)是超曲面的古典相对法,则相应的余法场U=(-(()f)/(()x_1),-(()f)/(()x_2),…,-(()f)/(()x_n),1).本文相对于余法向量场U^F=F(ρ)U又定义了一个相对法化,称之为M的F-相对法化,其中ρ=[det(f_(ij))]^(-1/(n+2)),并证明了F-相对极值超曲面的Bernstein性质.Let x ： M →R^n＋1 be a locally strongly convex hypersurface, given by the graph of a locally strongly convex function xn＋1 = f（x1,x2,... ,xn） defined in a convex domain Ω C Rn. Let Y --- （0, 0,… ,0, 1） denote the canonical relative normal of the hypersurface. Then the associated conormal field U = （- f/ x1,- f/ x2, …,- f/ xn, 1）. In this paper, we define another relative normalization in terms of the conormal vector field Uf = F（p）U, where p= 1 [det（fij）]-1/n＋2. It is called an F-relative normalization of M. We prove the Bernstein property for F-relative extremal hypersurfaces.

关 键 词：F-相对法化 F-相对度量 F-相对极值超曲面 

分 类 号：O186.13[理学—数学]